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curl -X POST \
  'http://laksa085.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://statisticsbyjim.com/probability/beta-distribution/\')), getAhrefsUnparsedNoserviceFromURL(\'https://statisticsbyjim.com/probability/beta-distribution/\'))) FORMAT JSONEachRow'

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{"found_url":"https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/","crawl_time":1776154775,"first_indexed_time":1652333513,"http_code":200,"src_unparsed":"com,statisticsbyjim!\/probability\/beta-distribution\/ s443","src_root_hash":"11135338449183465285","history_drop_reason":null,"meta_title":"Beta Distribution: Uses, Parameters & Examples - Statistics By Jim","meta_descriptions":["The beta distribution is a continuous probability distribution that models random variables with values falling inside a finite interval."],"attrs_boilerpipe_text":"The beta\ndistribution\nis a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in\nBayesian analysis\n.\nThe standard beta distribution uses the interval [0,1]. This range is ideal for modeling probabilities, particularly for experiments with only two outcomes. However, other intervals are possible.\nRelated post\n:\nUnderstanding Probability Distributions\nBeta Distribution Parameters and Notation\nUnlike other distributions with shape and scale\nparameters\n, the beta distribution has two shape parameters, α and β. Both parameters must be positive values.\nAdditionally,\nstatisticians\ndenote the finite interval’s upper and lower bounds as\na\nand\nb\n, respectively.\nLet’s see how these parameters work by graphing the\nprobability density function\nfor this distribution!\nHow to Calculate Beta Distribution Parameters\nStatistical software can use\nmaximum likelihood estimation\nto find the parameters for the beta distribution. This process\nestimates\nthe parameters that produce the best fitting curve for your data. Alternatively, you can perform simple calculations using the outcome of a binomial experiment to find the appropriate parameters, which I show in the next section.\nThe beta distribution is particularly flexible at modeling different curves within the interval, including symmetrical, left and\nright-skewed\n, U and inverted U shapes, and straight lines. The standard form can illustrate all curves, so I’ll use it in the examples below. However, keep in mind that the upper and lower bounds do not need to be 0 and 1.\nNote that my software refers to α and β as First and Second, respectively.\nBeta vs Binomial Distribution and Updating Prior Probabilities\nThe beta distribution has a close relationship with the binomial distribution. First, remember that the binomial distribution models the number of successes in a specific number of trials when you have binary data. Now, consider that the number of successes divided by the number of trials is a binomial proportion, which is a probability. The beta distribution models the likelihood of success in Bernoulli Trials and captures its uncertainty. Learn more about the\nBinomial Distribution\n.\nSuppose you sell breakfast cereal and perform a simple experiment. You randomly select ten people to try your cereal and a competitor’s. When a subject says your cereal is better, it’s a success. Seven out of 10 (70%) said your cereal is better. Because there are only two possible outcomes (success\/failure), it’s a binomial experiment. Let’s use the beta distribution to model the results.\nFor this type of experiment, calculate the beta parameters as follows:\nα = k + 1\nβ = n – k + 1\nWhere:\nk = number of successes\nn = number of trials.\nAdditionally, use this method to update your prior probabilities in a Bayesian analysis after you obtain additional information from a new binomial experiment. Simply add the new successes and trials to parameters of the prior probability’s beta distribution. As α and β increase, the distribution narrows, reflecting the greater precision of the larger\nsample size\n.\nFor our experiment, we have 7 successes and 10 trials:\nα = 7 + 1 = 8\nβ = 10 – 7 + 1 = 4\nAssessing the Results\nUsing these parameter values produces the following beta distribution.\nIn closing, I’ll emphasize the relationship between the beta and binomial distributions. The graph below displays the binomial distribution for our experiment. Notice the similarities? Both curves peak at 0.7 or 7\/10 and are similarly\nleft-skewed\n. In the binomial distribution, take the number of successes and divide by 10 (the number of trials) to obtain the probabilities in the beta distribution.","attrs_markdown":"- [Skip to secondary menu](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#genesis-nav-secondary)\n- [Skip to main content](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#genesis-content)\n- [Skip to primary sidebar](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#genesis-sidebar-primary)\n\n- [My Store](https:\/\/statisticsbyjim.com\/store\/)\n- [Glossary](https:\/\/statisticsbyjim.com\/glossary\/)\n- [Home](https:\/\/statisticsbyjim.com\/ \"Statistics by Jim\")\n- [About Me](https:\/\/statisticsbyjim.com\/jim_frost\/)\n- [Contact Me](https:\/\/statisticsbyjim.com\/contact_jim_frost\/)\n\n[Statistics By Jim](https:\/\/statisticsbyjim.com\/)\n\nMaking statistics intuitive\n\n- [Graphs](https:\/\/statisticsbyjim.com\/graphs\/)\n- [Basics](https:\/\/statisticsbyjim.com\/basics\/)\n- [Hypothesis Testing](https:\/\/statisticsbyjim.com\/hypothesis-testing\/)\n- [Regression](https:\/\/statisticsbyjim.com\/regression\/)\n- [ANOVA](https:\/\/statisticsbyjim.com\/anova\/)\n- [Probability](https:\/\/statisticsbyjim.com\/probability\/)\n- [Time Series](https:\/\/statisticsbyjim.com\/time-series\/)\n- [Fun](https:\/\/statisticsbyjim.com\/fun\/)\n- [Calculators](https:\/\/statisticsbyjim.com\/statistical_calculators\/)\n\n# Beta Distribution: Uses, Parameters & Examples\nBy [Jim Frost](https:\/\/statisticsbyjim.com\/author\/statis11_wp\/) [7 Comments](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comments)\n\nThe beta [distribution](https:\/\/statisticsbyjim.com\/glossary\/distribution\/) is a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in [Bayesian analysis](https:\/\/statisticsbyjim.com\/glossary\/bayesian-analysis\/).\n\nThe standard beta distribution uses the interval \\[0,1\\]. This range is ideal for modeling probabilities, particularly for experiments with only two outcomes. However, other intervals are possible.\n\n**Related post**: [Understanding Probability Distributions](https:\/\/statisticsbyjim.com\/basics\/probability-distributions\/)\n\n## Beta Distribution Parameters and Notation\nUnlike other distributions with shape and scale [parameters](https:\/\/statisticsbyjim.com\/glossary\/parameter\/), the beta distribution has two shape parameters, α and β. Both parameters must be positive values.\n\nAdditionally, [statisticians](https:\/\/statisticsbyjim.com\/glossary\/statistics\/) denote the finite interval’s upper and lower bounds as *a* and *b*, respectively.\n\nLet’s see how these parameters work by graphing the [probability density function](https:\/\/statisticsbyjim.com\/probability\/probability-density-function\/) for this distribution\\!\n\n### How to Calculate Beta Distribution Parameters\nStatistical software can use [maximum likelihood estimation](https:\/\/statisticsbyjim.com\/glossary\/maximum-likelihood-estimation-mle\/) to find the parameters for the beta distribution. This process [estimates](https:\/\/statisticsbyjim.com\/glossary\/estimator\/) the parameters that produce the best fitting curve for your data. Alternatively, you can perform simple calculations using the outcome of a binomial experiment to find the appropriate parameters, which I show in the next section.\n\nThe beta distribution is particularly flexible at modeling different curves within the interval, including symmetrical, left and [right-skewed](https:\/\/statisticsbyjim.com\/glossary\/skewness\/), U and inverted U shapes, and straight lines. The standard form can illustrate all curves, so I’ll use it in the examples below. However, keep in mind that the upper and lower bounds do not need to be 0 and 1.\n\n![Graph with examples of the beta distribution.](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%20576%20384'%3E%3C\/svg%3E)![Graph with examples of the beta distribution.](https:\/\/i0.wp.com\/statisticsbyjim.com\/wp-content\/uploads\/2022\/05\/beta_distribution_examples.png?resize=576%2C384&ssl=1)\n\nNote that my software refers to α and β as First and Second, respectively.\n\n## Beta vs Binomial Distribution and Updating Prior Probabilities\nThe beta distribution has a close relationship with the binomial distribution. First, remember that the binomial distribution models the number of successes in a specific number of trials when you have binary data. Now, consider that the number of successes divided by the number of trials is a binomial proportion, which is a probability. The beta distribution models the likelihood of success in Bernoulli Trials and captures its uncertainty. Learn more about the [Binomial Distribution](https:\/\/statisticsbyjim.com\/probability\/binomial-distribution\/).\n\nSuppose you sell breakfast cereal and perform a simple experiment. You randomly select ten people to try your cereal and a competitor’s. When a subject says your cereal is better, it’s a success. Seven out of 10 (70%) said your cereal is better. Because there are only two possible outcomes (success\/failure), it’s a binomial experiment. Let’s use the beta distribution to model the results.\n\nFor this type of experiment, calculate the beta parameters as follows:\n\n- α = k + 1\n- β = n – k + 1\n\nWhere:\n\n- k = number of successes\n- n = number of trials.\n\nAdditionally, use this method to update your prior probabilities in a Bayesian analysis after you obtain additional information from a new binomial experiment. Simply add the new successes and trials to parameters of the prior probability’s beta distribution. As α and β increase, the distribution narrows, reflecting the greater precision of the larger [sample size](https:\/\/statisticsbyjim.com\/glossary\/sample-size\/).\n\nFor our experiment, we have 7 successes and 10 trials:\n\n- α = 7 + 1 = 8\n- β = 10 – 7 + 1 = 4\n### Assessing the Results\nUsing these parameter values produces the following beta distribution.\n\n![Graph displaying the beta distribution of probabilities for the example experiment.](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%20576%20384'%3E%3C\/svg%3E)![Graph displaying the beta distribution of probabilities for the example experiment.](https:\/\/i0.wp.com\/statisticsbyjim.com\/wp-content\/uploads\/2022\/05\/beta_distribution_experiment.png?resize=576%2C384&ssl=1)\n\nIn closing, I’ll emphasize the relationship between the beta and binomial distributions. The graph below displays the binomial distribution for our experiment. Notice the similarities? Both curves peak at 0.7 or 7\/10 and are similarly [left-skewed](https:\/\/statisticsbyjim.com\/basics\/skewed-distribution\/). In the binomial distribution, take the number of successes and divide by 10 (the number of trials) to obtain the probabilities in the beta distribution.\n\n![Graph of the binomial distribution for the example experiment.](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%20576%20384'%3E%3C\/svg%3E)![Graph of the binomial distribution for the example experiment.](https:\/\/i0.wp.com\/statisticsbyjim.com\/wp-content\/uploads\/2022\/05\/binomial_experiment_distribution.png?resize=576%2C384&ssl=1)\n\n### Share this:\n- [Tweet](https:\/\/twitter.com\/share)\n- [![](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%200%200'%3E%3C\/svg%3E)![](https:\/\/i0.wp.com\/assets.pinterest.com\/images\/pidgets\/pinit_fg_en_rect_gray_20.png)](https:\/\/www.pinterest.com\/pin\/create\/button\/?url=https%3A%2F%2Fstatisticsbyjim.com%2Fprobability%2Fbeta-distribution%2F&media=https%3A%2F%2Fi0.wp.com%2Fstatisticsbyjim.com%2Fwp-content%2Fuploads%2F2022%2F05%2Fbeta_distribution_examples.png%3Ffit%3D576%252C384%26ssl%3D1&description=Beta%20Distribution%3A%20Uses%2C%20Parameters%20%26%20Examples)\n\n### Like this:\nLike Loading...\n### *Related*\n\nFiled Under: [Probability](https:\/\/statisticsbyjim.com\/probability\/) Tagged With: [conceptual](https:\/\/statisticsbyjim.com\/tag\/conceptual\/), [distributions](https:\/\/statisticsbyjim.com\/tag\/distributions\/), [graphs](https:\/\/statisticsbyjim.com\/tag\/graphs\/)\n## Reader Interactions\n### Comments\n1. ![](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%2060%2060'%3E%3C\/svg%3E)![](https:\/\/secure.gravatar.com\/avatar\/5942ce9c8d9e1ddad942fc3c7442fa09dc3afa1232951d38efb33200982bfdde?s=60&d=mm&r=g)Pradeep Kandpal says\n   \n   [September 19, 2024 at 12:57 am](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-12770)\n   \n   Thanks a ton, Jim. I was using excel’s beta.inv function to simulate a random variable from a dataset that follows a beta distributon and was wondering how the [alpha](https:\/\/statisticsbyjim.com\/glossary\/significance-level\/) and beta value are arrived at.\n   \n   Loading...\n   \n   [Reply](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-12770)\n2. ![](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%2060%2060'%3E%3C\/svg%3E)![](https:\/\/secure.gravatar.com\/avatar\/a181ea4794c29b95a8d636b18494b898a6c824f865e6c41789042e7d02d8d068?s=60&d=mm&r=g)Norman Abraham says\n   \n   [March 18, 2023 at 8:12 am](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11425)\n   \n   Re: A flexible method for parameterizing ranked nodes in Bayesian networks using Beta distributions, Steven Mascaro and Owen Woodberry\n   \n   Hello,\n   \n   I would appreciate your comments regarding the above as to its comparison to the Ranked Node Method of Fenton and Neil.\n   \n   Thank you,\n   \n   Norm\n   \n   Loading...\n   \n   [Reply](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11425)\n   - ![](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%2060%2060'%3E%3C\/svg%3E)![](https:\/\/secure.gravatar.com\/avatar\/ced98a97d5c423fc1dfd866dbd5bfbfa2193694ca0bddd9b84fd2e5c846ccc4c?s=60&d=mm&r=g)Jim Frost says\n     \n     [March 18, 2023 at 10:14 pm](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11426)\n     \n     Hi Norman, unfortunately, I’m not familiar with that method. Sorry.\n     \n     Loading...\n     \n     [Reply](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11426)\n3. ![](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%2060%2060'%3E%3C\/svg%3E)![](https:\/\/secure.gravatar.com\/avatar\/320b5ac5ed399aa2da962d7aaac0412b4f5f04a26f237f36e8da04a15e3fed75?s=60&d=mm&r=g)Pierre V says\n   \n   [December 10, 2022 at 10:28 am](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11315)\n   \n   Hello Jim,  \n    Thank you for you explanation. I am using Minitab too and I am trying to know which distribution fits the best my data. I already computed the identification of the law and none of the laws studied were ok (p-values smaller than 0,05).  \n    I would like to know if my data fits a beta distribution but I do not know how to proceed. Please let me know if it is possible\n   \n   Loading...\n   \n   [Reply](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11315)\n   - ![](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%2060%2060'%3E%3C\/svg%3E)![](https:\/\/secure.gravatar.com\/avatar\/ced98a97d5c423fc1dfd866dbd5bfbfa2193694ca0bddd9b84fd2e5c846ccc4c?s=60&d=mm&r=g)Jim Frost says\n     \n     [December 10, 2022 at 6:04 pm](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11317)\n     \n     Hi Pierre,\n     \n     When you say “laws,” do you mean probability distributions? Laws is not really the correct word. It’s better to say probability distributions or function. Although, I realize that English might not be your first language. I just want to be sure that I understand the question. You mention determining whether your data fit the Beta distribution, but I’ll address your question in relation to all candidate distributions. After all, if your data don’t fit the Beta distribution, it might fit another.\n     \n     If none of the candidate probability distributions fit your data, that’s a tough spot to be in. Here are two possibilities to consider.\n     \n     Have you’ve also looked at the data transformations to see if they normalize your data?\n     \n     Is your [sample](https:\/\/statisticsbyjim.com\/glossary\/sample\/) size fairly large? If so, the distribution tests might be flagging trivial departures from the probability distributions. Check the probability distribution plots. If you have a large sample size but the data points follow the straight line in a probability distribution plot, it’s evidence that your data follow that distribution even if the [p-value](https:\/\/statisticsbyjim.com\/glossary\/p-value\/) is less than 0.05. For more information, read my post about [probability distribution plots](https:\/\/statisticsbyjim.com\/basics\/assessing-normality-histograms-probability-plots\/). That article focuses on the normal distribution, but the same ideas apply to the other distributions.\n     \n     If those two points don’t help you out, I unfortunately don’t have any easy answers for you because this type of issue highly depends on the subject area. You might also research your subject area to determine what others have found. They might have helpful insights.\n     \n     When your data don’t fit a known distribution, you might need to analyze them using either a nonparametric analysis or by bootstrapping. Those methods don’t assume that your data follow a particular distribution.\n     \n     I wish I could provide you with more concrete help, but I hope that points you in the right direction\\!\n     \n     Loading...\n     \n     [Reply](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11317)\n4. ![](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%2060%2060'%3E%3C\/svg%3E)![](https:\/\/secure.gravatar.com\/avatar\/47f9a50daf0ced9a2d84c31ab6298e1527cb1e1a29beb0334881607f59ef1a6c?s=60&d=mm&r=g)Khaled Alrashidi says\n   \n   [September 27, 2022 at 6:43 am](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11098)\n   \n   Thank you, Jim, for a clear explanation to the beta distribution! I wanted to ensure I understood the example: Shouldn’t beta be 2 instead of 4 since 10 – 7 + 1 = 2? Please let me know if I got this right.\n   \n   Loading...\n   \n   [Reply](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11098)\n   - ![](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%2060%2060'%3E%3C\/svg%3E)![](https:\/\/secure.gravatar.com\/avatar\/ced98a97d5c423fc1dfd866dbd5bfbfa2193694ca0bddd9b84fd2e5c846ccc4c?s=60&d=mm&r=g)Jim Frost says\n     \n     [September 27, 2022 at 2:02 pm](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11099)\n     \n     Hi Khaled,\n     \n     Using the standard order of operations, it equals 4 because addition and subtraction have equal priority in the expression. Consequently, you just proceed from left to right. Type that into Excel to confirm that the result is 4. If I had put parentheses around (7 + 1), then the answer would’ve been 2.\n     \n     Loading...\n     \n     [Reply](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#comment-11099)\n### Comments and Questions[Cancel reply](https:\/\/statisticsbyjim.com\/probability\/beta-distribution\/#respond)\n\n## Primary Sidebar\n### Meet Jim\nI’ll help you intuitively understand statistics by focusing on concepts and using plain English so you can concentrate on understanding your results.\n\n[Read More...](https:\/\/statisticsbyjim.com\/jim_frost\/)\n\n### Buy My Introduction to Statistics Book\\!\n[![Cover of my Introduction to Statistics: An Intuitive Guide ebook.](data:image\/svg+xml,%3Csvg%20xmlns='http:\/\/www.w3.org\/2000\/svg'%20viewBox='0%200%20200%20300'%3E%3C\/svg%3E)![Cover of my Introduction to Statistics: An Intuitive Guide 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[Comparing Regression Lines with Hypothesis Tests](https:\/\/statisticsbyjim.com\/regression\/comparing-regression-lines\/#comment-13112)\n- Jim Frost on [Pareto Chart: Making, Reading & Examples](https:\/\/statisticsbyjim.com\/graphs\/pareto-charts\/#comment-13110)\n- mphatso lazaro on [Pareto Chart: Making, Reading & Examples](https:\/\/statisticsbyjim.com\/graphs\/pareto-charts\/#comment-13109)\n\nCopyright © 2026 · Jim Frost · [Privacy Policy](https:\/\/statisticsbyjim.com\/privacy-policy\/)\n\n%d","attrs_readable_markdown":"The beta [distribution](https:\/\/statisticsbyjim.com\/glossary\/distribution\/) is a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in [Bayesian analysis](https:\/\/statisticsbyjim.com\/glossary\/bayesian-analysis\/).\n\nThe standard beta distribution uses the interval \\[0,1\\]. This range is ideal for modeling probabilities, particularly for experiments with only two outcomes. However, other intervals are possible.\n\n**Related post**: [Understanding Probability Distributions](https:\/\/statisticsbyjim.com\/basics\/probability-distributions\/)\n\n## Beta Distribution Parameters and Notation\nUnlike other distributions with shape and scale [parameters](https:\/\/statisticsbyjim.com\/glossary\/parameter\/), the beta distribution has two shape parameters, α and β. Both parameters must be positive values.\n\nAdditionally, [statisticians](https:\/\/statisticsbyjim.com\/glossary\/statistics\/) denote the finite interval’s upper and lower bounds as *a* and *b*, respectively.\n\nLet’s see how these parameters work by graphing the [probability density function](https:\/\/statisticsbyjim.com\/probability\/probability-density-function\/) for this distribution\\!\n\n### How to Calculate Beta Distribution Parameters\nStatistical software can use [maximum likelihood estimation](https:\/\/statisticsbyjim.com\/glossary\/maximum-likelihood-estimation-mle\/) to find the parameters for the beta distribution. This process [estimates](https:\/\/statisticsbyjim.com\/glossary\/estimator\/) the parameters that produce the best fitting curve for your data. Alternatively, you can perform simple calculations using the outcome of a binomial experiment to find the appropriate parameters, which I show in the next section.\n\nThe beta distribution is particularly flexible at modeling different curves within the interval, including symmetrical, left and [right-skewed](https:\/\/statisticsbyjim.com\/glossary\/skewness\/), U and inverted U shapes, and straight lines. The standard form can illustrate all curves, so I’ll use it in the examples below. However, keep in mind that the upper and lower bounds do not need to be 0 and 1.\n\n![Graph with examples of the beta distribution.](https:\/\/i0.wp.com\/statisticsbyjim.com\/wp-content\/uploads\/2022\/05\/beta_distribution_examples.png?resize=576%2C384&ssl=1)\n\nNote that my software refers to α and β as First and Second, respectively.\n\n## Beta vs Binomial Distribution and Updating Prior Probabilities\nThe beta distribution has a close relationship with the binomial distribution. First, remember that the binomial distribution models the number of successes in a specific number of trials when you have binary data. Now, consider that the number of successes divided by the number of trials is a binomial proportion, which is a probability. The beta distribution models the likelihood of success in Bernoulli Trials and captures its uncertainty. Learn more about the [Binomial Distribution](https:\/\/statisticsbyjim.com\/probability\/binomial-distribution\/).\n\nSuppose you sell breakfast cereal and perform a simple experiment. You randomly select ten people to try your cereal and a competitor’s. When a subject says your cereal is better, it’s a success. Seven out of 10 (70%) said your cereal is better. Because there are only two possible outcomes (success\/failure), it’s a binomial experiment. Let’s use the beta distribution to model the results.\n\nFor this type of experiment, calculate the beta parameters as follows:\n\n- α = k + 1\n- β = n – k + 1\n\nWhere:\n\n- k = number of successes\n- n = number of trials.\n\nAdditionally, use this method to update your prior probabilities in a Bayesian analysis after you obtain additional information from a new binomial experiment. Simply add the new successes and trials to parameters of the prior probability’s beta distribution. As α and β increase, the distribution narrows, reflecting the greater precision of the larger [sample size](https:\/\/statisticsbyjim.com\/glossary\/sample-size\/).\n\nFor our experiment, we have 7 successes and 10 trials:\n\n- α = 7 + 1 = 8\n- β = 10 – 7 + 1 = 4\n### Assessing the Results\nUsing these parameter values produces the following beta distribution.\n\n![Graph displaying the beta distribution of probabilities for the example experiment.](https:\/\/i0.wp.com\/statisticsbyjim.com\/wp-content\/uploads\/2022\/05\/beta_distribution_experiment.png?resize=576%2C384&ssl=1)\n\nIn closing, I’ll emphasize the relationship between the beta and binomial distributions. The graph below displays the binomial distribution for our experiment. Notice the similarities? Both curves peak at 0.7 or 7\/10 and are similarly [left-skewed](https:\/\/statisticsbyjim.com\/basics\/skewed-distribution\/). In the binomial distribution, take the number of successes and divide by 10 (the number of trials) to obtain the probabilities in the beta distribution.\n\n![Graph of the binomial distribution for the example experiment.](https:\/\/i0.wp.com\/statisticsbyjim.com\/wp-content\/uploads\/2022\/05\/binomial_experiment_distribution.png?resize=576%2C384&ssl=1)","meta_canonical":null}

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Boilerpipe Text	The beta distribution is a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in Bayesian analysis . The standard beta distribution uses the interval [0,1]. This range is ideal for modeling probabilities, particularly for experiments with only two outcomes. However, other intervals are possible. Related post : Understanding Probability Distributions Beta Distribution Parameters and Notation Unlike other distributions with shape and scale parameters , the beta distribution has two shape parameters, α and β. Both parameters must be positive values. Additionally, statisticians denote the finite interval’s upper and lower bounds as a and b , respectively. Let’s see how these parameters work by graphing the probability density function for this distribution! How to Calculate Beta Distribution Parameters Statistical software can use maximum likelihood estimation to find the parameters for the beta distribution. This process estimates the parameters that produce the best fitting curve for your data. Alternatively, you can perform simple calculations using the outcome of a binomial experiment to find the appropriate parameters, which I show in the next section. The beta distribution is particularly flexible at modeling different curves within the interval, including symmetrical, left and right-skewed , U and inverted U shapes, and straight lines. The standard form can illustrate all curves, so I’ll use it in the examples below. However, keep in mind that the upper and lower bounds do not need to be 0 and 1. Note that my software refers to α and β as First and Second, respectively. Beta vs Binomial Distribution and Updating Prior Probabilities The beta distribution has a close relationship with the binomial distribution. First, remember that the binomial distribution models the number of successes in a specific number of trials when you have binary data. Now, consider that the number of successes divided by the number of trials is a binomial proportion, which is a probability. The beta distribution models the likelihood of success in Bernoulli Trials and captures its uncertainty. Learn more about the Binomial Distribution . Suppose you sell breakfast cereal and perform a simple experiment. You randomly select ten people to try your cereal and a competitor’s. When a subject says your cereal is better, it’s a success. Seven out of 10 (70%) said your cereal is better. Because there are only two possible outcomes (success/failure), it’s a binomial experiment. Let’s use the beta distribution to model the results. For this type of experiment, calculate the beta parameters as follows: α = k + 1 β = n – k + 1 Where: k = number of successes n = number of trials. Additionally, use this method to update your prior probabilities in a Bayesian analysis after you obtain additional information from a new binomial experiment. Simply add the new successes and trials to parameters of the prior probability’s beta distribution. As α and β increase, the distribution narrows, reflecting the greater precision of the larger sample size . For our experiment, we have 7 successes and 10 trials: α = 7 + 1 = 8 β = 10 – 7 + 1 = 4 Assessing the Results Using these parameter values produces the following beta distribution. In closing, I’ll emphasize the relationship between the beta and binomial distributions. The graph below displays the binomial distribution for our experiment. Notice the similarities? Both curves peak at 0.7 or 7/10 and are similarly left-skewed . In the binomial distribution, take the number of successes and divide by 10 (the number of trials) to obtain the probabilities in the beta distribution.
Markdown	- [Skip to secondary menu](https://statisticsbyjim.com/probability/beta-distribution/#genesis-nav-secondary) - [Skip to main content](https://statisticsbyjim.com/probability/beta-distribution/#genesis-content) - [Skip to primary sidebar](https://statisticsbyjim.com/probability/beta-distribution/#genesis-sidebar-primary) - [My Store](https://statisticsbyjim.com/store/) - [Glossary](https://statisticsbyjim.com/glossary/) - [Home](https://statisticsbyjim.com/ "Statistics by Jim") - [About Me](https://statisticsbyjim.com/jim_frost/) - [Contact Me](https://statisticsbyjim.com/contact_jim_frost/) [Statistics By Jim](https://statisticsbyjim.com/) Making statistics intuitive - [Graphs](https://statisticsbyjim.com/graphs/) - [Basics](https://statisticsbyjim.com/basics/) - [Hypothesis Testing](https://statisticsbyjim.com/hypothesis-testing/) - [Regression](https://statisticsbyjim.com/regression/) - [ANOVA](https://statisticsbyjim.com/anova/) - [Probability](https://statisticsbyjim.com/probability/) - [Time Series](https://statisticsbyjim.com/time-series/) - [Fun](https://statisticsbyjim.com/fun/) - [Calculators](https://statisticsbyjim.com/statistical_calculators/) # Beta Distribution: Uses, Parameters & Examples By [Jim Frost](https://statisticsbyjim.com/author/statis11_wp/) [7 Comments](https://statisticsbyjim.com/probability/beta-distribution/#comments) The beta [distribution](https://statisticsbyjim.com/glossary/distribution/) is a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in [Bayesian analysis](https://statisticsbyjim.com/glossary/bayesian-analysis/). The standard beta distribution uses the interval \[0,1\]. This range is ideal for modeling probabilities, particularly for experiments with only two outcomes. However, other intervals are possible. Related post: [Understanding Probability Distributions](https://statisticsbyjim.com/basics/probability-distributions/) ## Beta Distribution Parameters and Notation Unlike other distributions with shape and scale [parameters](https://statisticsbyjim.com/glossary/parameter/), the beta distribution has two shape parameters, α and β. Both parameters must be positive values. Additionally, [statisticians](https://statisticsbyjim.com/glossary/statistics/) denote the finite interval’s upper and lower bounds as a and b, respectively. Let’s see how these parameters work by graphing the [probability density function](https://statisticsbyjim.com/probability/probability-density-function/) for this distribution\! ### How to Calculate Beta Distribution Parameters Statistical software can use [maximum likelihood estimation](https://statisticsbyjim.com/glossary/maximum-likelihood-estimation-mle/) to find the parameters for the beta distribution. This process [estimates](https://statisticsbyjim.com/glossary/estimator/) the parameters that produce the best fitting curve for your data. Alternatively, you can perform simple calculations using the outcome of a binomial experiment to find the appropriate parameters, which I show in the next section. The beta distribution is particularly flexible at modeling different curves within the interval, including symmetrical, left and [right-skewed](https://statisticsbyjim.com/glossary/skewness/), U and inverted U shapes, and straight lines. The standard form can illustrate all curves, so I’ll use it in the examples below. However, keep in mind that the upper and lower bounds do not need to be 0 and 1. ![Graph with examples of the beta distribution.](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20576%20384'%3E%3C/svg%3E)![Graph with examples of the beta distribution.](https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2022/05/beta_distribution_examples.png?resize=576%2C384&ssl=1) Note that my software refers to α and β as First and Second, respectively. ## Beta vs Binomial Distribution and Updating Prior Probabilities The beta distribution has a close relationship with the binomial distribution. First, remember that the binomial distribution models the number of successes in a specific number of trials when you have binary data. Now, consider that the number of successes divided by the number of trials is a binomial proportion, which is a probability. The beta distribution models the likelihood of success in Bernoulli Trials and captures its uncertainty. Learn more about the [Binomial Distribution](https://statisticsbyjim.com/probability/binomial-distribution/). Suppose you sell breakfast cereal and perform a simple experiment. You randomly select ten people to try your cereal and a competitor’s. When a subject says your cereal is better, it’s a success. Seven out of 10 (70%) said your cereal is better. Because there are only two possible outcomes (success/failure), it’s a binomial experiment. Let’s use the beta distribution to model the results. For this type of experiment, calculate the beta parameters as follows: - α = k + 1 - β = n – k + 1 Where: - k = number of successes - n = number of trials. Additionally, use this method to update your prior probabilities in a Bayesian analysis after you obtain additional information from a new binomial experiment. Simply add the new successes and trials to parameters of the prior probability’s beta distribution. As α and β increase, the distribution narrows, reflecting the greater precision of the larger [sample size](https://statisticsbyjim.com/glossary/sample-size/). For our experiment, we have 7 successes and 10 trials: - α = 7 + 1 = 8 - β = 10 – 7 + 1 = 4 ### Assessing the Results Using these parameter values produces the following beta distribution. ![Graph displaying the beta distribution of probabilities for the example experiment.](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20576%20384'%3E%3C/svg%3E)![Graph displaying the beta distribution of probabilities for the example experiment.](https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2022/05/beta_distribution_experiment.png?resize=576%2C384&ssl=1) In closing, I’ll emphasize the relationship between the beta and binomial distributions. The graph below displays the binomial distribution for our experiment. Notice the similarities? Both curves peak at 0.7 or 7/10 and are similarly [left-skewed](https://statisticsbyjim.com/basics/skewed-distribution/). In the binomial distribution, take the number of successes and divide by 10 (the number of trials) to obtain the probabilities in the beta distribution. ![Graph of the binomial distribution for the example experiment.](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20576%20384'%3E%3C/svg%3E)![Graph of the binomial distribution for the example experiment.](https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2022/05/binomial_experiment_distribution.png?resize=576%2C384&ssl=1) ### Share this: - [Tweet](https://twitter.com/share) - [![](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%200%200'%3E%3C/svg%3E)![](https://i0.wp.com/assets.pinterest.com/images/pidgets/pinit_fg_en_rect_gray_20.png)](https://www.pinterest.com/pin/create/button/?url=https%3A%2F%2Fstatisticsbyjim.com%2Fprobability%2Fbeta-distribution%2F&media=https%3A%2F%2Fi0.wp.com%2Fstatisticsbyjim.com%2Fwp-content%2Fuploads%2F2022%2F05%2Fbeta_distribution_examples.png%3Ffit%3D576%252C384%26ssl%3D1&description=Beta%20Distribution%3A%20Uses%2C%20Parameters%20%26%20Examples) ### Like this: Like Loading... ### Related Filed Under: [Probability](https://statisticsbyjim.com/probability/) Tagged With: [conceptual](https://statisticsbyjim.com/tag/conceptual/), [distributions](https://statisticsbyjim.com/tag/distributions/), [graphs](https://statisticsbyjim.com/tag/graphs/) ## Reader Interactions ### Comments 1. ![](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2060%2060'%3E%3C/svg%3E)![](https://secure.gravatar.com/avatar/5942ce9c8d9e1ddad942fc3c7442fa09dc3afa1232951d38efb33200982bfdde?s=60&d=mm&r=g)Pradeep Kandpal says [September 19, 2024 at 12:57 am](https://statisticsbyjim.com/probability/beta-distribution/#comment-12770) Thanks a ton, Jim. I was using excel’s beta.inv function to simulate a random variable from a dataset that follows a beta distributon and was wondering how the [alpha](https://statisticsbyjim.com/glossary/significance-level/) and beta value are arrived at. Loading... [Reply](https://statisticsbyjim.com/probability/beta-distribution/#comment-12770) 2. ![](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2060%2060'%3E%3C/svg%3E)![](https://secure.gravatar.com/avatar/a181ea4794c29b95a8d636b18494b898a6c824f865e6c41789042e7d02d8d068?s=60&d=mm&r=g)Norman Abraham says [March 18, 2023 at 8:12 am](https://statisticsbyjim.com/probability/beta-distribution/#comment-11425) Re: A flexible method for parameterizing ranked nodes in Bayesian networks using Beta distributions, Steven Mascaro and Owen Woodberry Hello, I would appreciate your comments regarding the above as to its comparison to the Ranked Node Method of Fenton and Neil. Thank you, Norm Loading... [Reply](https://statisticsbyjim.com/probability/beta-distribution/#comment-11425) - ![](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2060%2060'%3E%3C/svg%3E)![](https://secure.gravatar.com/avatar/ced98a97d5c423fc1dfd866dbd5bfbfa2193694ca0bddd9b84fd2e5c846ccc4c?s=60&d=mm&r=g)Jim Frost says [March 18, 2023 at 10:14 pm](https://statisticsbyjim.com/probability/beta-distribution/#comment-11426) Hi Norman, unfortunately, I’m not familiar with that method. Sorry. Loading... [Reply](https://statisticsbyjim.com/probability/beta-distribution/#comment-11426) 3. ![](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2060%2060'%3E%3C/svg%3E)![](https://secure.gravatar.com/avatar/320b5ac5ed399aa2da962d7aaac0412b4f5f04a26f237f36e8da04a15e3fed75?s=60&d=mm&r=g)Pierre V says [December 10, 2022 at 10:28 am](https://statisticsbyjim.com/probability/beta-distribution/#comment-11315) Hello Jim, Thank you for you explanation. I am using Minitab too and I am trying to know which distribution fits the best my data. I already computed the identification of the law and none of the laws studied were ok (p-values smaller than 0,05). I would like to know if my data fits a beta distribution but I do not know how to proceed. Please let me know if it is possible Loading... [Reply](https://statisticsbyjim.com/probability/beta-distribution/#comment-11315) - ![](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2060%2060'%3E%3C/svg%3E)![](https://secure.gravatar.com/avatar/ced98a97d5c423fc1dfd866dbd5bfbfa2193694ca0bddd9b84fd2e5c846ccc4c?s=60&d=mm&r=g)Jim Frost says [December 10, 2022 at 6:04 pm](https://statisticsbyjim.com/probability/beta-distribution/#comment-11317) Hi Pierre, When you say “laws,” do you mean probability distributions? Laws is not really the correct word. It’s better to say probability distributions or function. Although, I realize that English might not be your first language. I just want to be sure that I understand the question. You mention determining whether your data fit the Beta distribution, but I’ll address your question in relation to all candidate distributions. After all, if your data don’t fit the Beta distribution, it might fit another. If none of the candidate probability distributions fit your data, that’s a tough spot to be in. Here are two possibilities to consider. Have you’ve also looked at the data transformations to see if they normalize your data? Is your [sample](https://statisticsbyjim.com/glossary/sample/) size fairly large? If so, the distribution tests might be flagging trivial departures from the probability distributions. Check the probability distribution plots. If you have a large sample size but the data points follow the straight line in a probability distribution plot, it’s evidence that your data follow that distribution even if the [p-value](https://statisticsbyjim.com/glossary/p-value/) is less than 0.05. For more information, read my post about [probability distribution plots](https://statisticsbyjim.com/basics/assessing-normality-histograms-probability-plots/). That article focuses on the normal distribution, but the same ideas apply to the other distributions. If those two points don’t help you out, I unfortunately don’t have any easy answers for you because this type of issue highly depends on the subject area. You might also research your subject area to determine what others have found. They might have helpful insights. When your data don’t fit a known distribution, you might need to analyze them using either a nonparametric analysis or by bootstrapping. Those methods don’t assume that your data follow a particular distribution. I wish I could provide you with more concrete help, but I hope that points you in the right direction\! Loading... [Reply](https://statisticsbyjim.com/probability/beta-distribution/#comment-11317) 4. ![](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2060%2060'%3E%3C/svg%3E)![](https://secure.gravatar.com/avatar/47f9a50daf0ced9a2d84c31ab6298e1527cb1e1a29beb0334881607f59ef1a6c?s=60&d=mm&r=g)Khaled Alrashidi says [September 27, 2022 at 6:43 am](https://statisticsbyjim.com/probability/beta-distribution/#comment-11098) Thank you, Jim, for a clear explanation to the beta distribution! I wanted to ensure I understood the example: Shouldn’t beta be 2 instead of 4 since 10 – 7 + 1 = 2? Please let me know if I got this right. Loading... [Reply](https://statisticsbyjim.com/probability/beta-distribution/#comment-11098) - ![](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%2060%2060'%3E%3C/svg%3E)![](https://secure.gravatar.com/avatar/ced98a97d5c423fc1dfd866dbd5bfbfa2193694ca0bddd9b84fd2e5c846ccc4c?s=60&d=mm&r=g)Jim Frost says [September 27, 2022 at 2:02 pm](https://statisticsbyjim.com/probability/beta-distribution/#comment-11099) Hi Khaled, Using the standard order of operations, it equals 4 because addition and subtraction have equal priority in the expression. Consequently, you just proceed from left to right. Type that into Excel to confirm that the result is 4. If I had put parentheses around (7 + 1), then the answer would’ve been 2. Loading... 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Readable Markdown	The beta [distribution](https://statisticsbyjim.com/glossary/distribution/) is a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in [Bayesian analysis](https://statisticsbyjim.com/glossary/bayesian-analysis/). The standard beta distribution uses the interval \[0,1\]. This range is ideal for modeling probabilities, particularly for experiments with only two outcomes. However, other intervals are possible. Related post: [Understanding Probability Distributions](https://statisticsbyjim.com/basics/probability-distributions/) ## Beta Distribution Parameters and Notation Unlike other distributions with shape and scale [parameters](https://statisticsbyjim.com/glossary/parameter/), the beta distribution has two shape parameters, α and β. Both parameters must be positive values. Additionally, [statisticians](https://statisticsbyjim.com/glossary/statistics/) denote the finite interval’s upper and lower bounds as a and b, respectively. Let’s see how these parameters work by graphing the [probability density function](https://statisticsbyjim.com/probability/probability-density-function/) for this distribution\! ### How to Calculate Beta Distribution Parameters Statistical software can use [maximum likelihood estimation](https://statisticsbyjim.com/glossary/maximum-likelihood-estimation-mle/) to find the parameters for the beta distribution. This process [estimates](https://statisticsbyjim.com/glossary/estimator/) the parameters that produce the best fitting curve for your data. Alternatively, you can perform simple calculations using the outcome of a binomial experiment to find the appropriate parameters, which I show in the next section. The beta distribution is particularly flexible at modeling different curves within the interval, including symmetrical, left and [right-skewed](https://statisticsbyjim.com/glossary/skewness/), U and inverted U shapes, and straight lines. The standard form can illustrate all curves, so I’ll use it in the examples below. However, keep in mind that the upper and lower bounds do not need to be 0 and 1. ![Graph with examples of the beta distribution.](https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2022/05/beta_distribution_examples.png?resize=576%2C384&ssl=1) Note that my software refers to α and β as First and Second, respectively. ## Beta vs Binomial Distribution and Updating Prior Probabilities The beta distribution has a close relationship with the binomial distribution. First, remember that the binomial distribution models the number of successes in a specific number of trials when you have binary data. Now, consider that the number of successes divided by the number of trials is a binomial proportion, which is a probability. The beta distribution models the likelihood of success in Bernoulli Trials and captures its uncertainty. Learn more about the [Binomial Distribution](https://statisticsbyjim.com/probability/binomial-distribution/). Suppose you sell breakfast cereal and perform a simple experiment. You randomly select ten people to try your cereal and a competitor’s. When a subject says your cereal is better, it’s a success. Seven out of 10 (70%) said your cereal is better. Because there are only two possible outcomes (success/failure), it’s a binomial experiment. Let’s use the beta distribution to model the results. For this type of experiment, calculate the beta parameters as follows: - α = k + 1 - β = n – k + 1 Where: - k = number of successes - n = number of trials. Additionally, use this method to update your prior probabilities in a Bayesian analysis after you obtain additional information from a new binomial experiment. Simply add the new successes and trials to parameters of the prior probability’s beta distribution. As α and β increase, the distribution narrows, reflecting the greater precision of the larger [sample size](https://statisticsbyjim.com/glossary/sample-size/). For our experiment, we have 7 successes and 10 trials: - α = 7 + 1 = 8 - β = 10 – 7 + 1 = 4 ### Assessing the Results Using these parameter values produces the following beta distribution. ![Graph displaying the beta distribution of probabilities for the example experiment.](https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2022/05/beta_distribution_experiment.png?resize=576%2C384&ssl=1) In closing, I’ll emphasize the relationship between the beta and binomial distributions. The graph below displays the binomial distribution for our experiment. Notice the similarities? Both curves peak at 0.7 or 7/10 and are similarly [left-skewed](https://statisticsbyjim.com/basics/skewed-distribution/). In the binomial distribution, take the number of successes and divide by 10 (the number of trials) to obtain the probabilities in the beta distribution. ![Graph of the binomial distribution for the example experiment.](https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2022/05/binomial_experiment_distribution.png?resize=576%2C384&ssl=1)
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