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| Property | Value |
|---|---|
| URL | https://homepage.divms.uiowa.edu/~mbognar/applets/beta.html |
| Last Crawled | 2026-03-30 13:03:28 (19 days ago) |
| First Indexed | 2018-06-20 20:14:25 (7 years ago) |
| HTTP Status Code | 200 |
| Meta Title | Beta Distribution Applet/Calculator |
| Meta Description | null |
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| Boilerpipe Text | This applet computes probabilities and percentiles for beta random variables:
$$X \sim Beta(\alpha, \beta)$$
Directions
Enter the shape $\alpha$ and the shape $\beta$.
To compute a left-tail probability, select $P(X \lt x)$ from the drop-down box,
enter a numeric $x$ value in the
blue
box and press "Enter" or "Tab" on your keyboard. The probability $P(X \lt x)$ will appear in the
pink
box.
Select $P(X \gt x)$ from the drop-down box for a right-tail probability.
To determine a percentile, enter the percentile (e.g. use 0.8 for the 80th percentile) in the
pink
box and select $P(X \lt x)$ from the drop-down box and press "Tab" or "Enter" on your keyboard.
The percentile $x$ will appear in the
blue
box.
On the graph, the $x$ value appears in
blue
while the probability is shaded in
pink
.
Details
Probability density function
$$f(x)=\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)} x^{\alpha-1} (1-x)^{\beta-1}$$
where $0 \le x \le 1$, $\alpha > 0$, and $\beta > 0$
$\mu=E(X)=\frac{\alpha}{\alpha+\beta}$
$\sigma^2=Var(X)=\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}$
$\sigma=SD(X)=\sqrt{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}}$ |
| Markdown | ### Beta Distribution \$X \\sim Beta(\\alpha, \\beta)\$
Help
©2025 Matt Bognar
Department of Statistics and Actuarial Science
University of Iowa
This applet computes probabilities and percentiles for beta random variables: \$\$X \\sim Beta(\\alpha, \\beta)\$\$
#### Directions
- Enter the shape \$\\alpha\$ and the shape \$\\beta\$.
- To compute a left-tail probability, select \$P(X \\lt x)\$ from the drop-down box, enter a numeric \$x\$ value in the blue box and press "Enter" or "Tab" on your keyboard. The probability \$P(X \\lt x)\$ will appear in the pink box. Select \$P(X \\gt x)\$ from the drop-down box for a right-tail probability.
- To determine a percentile, enter the percentile (e.g. use 0.8 for the 80th percentile) in the pink box and select \$P(X \\lt x)\$ from the drop-down box and press "Tab" or "Enter" on your keyboard. The percentile \$x\$ will appear in the blue box.
On the graph, the \$x\$ value appears in blue while the probability is shaded in pink.
#### Details
- Probability density function \$\$f(x)=\\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} x^{\\alpha-1} (1-x)^{\\beta-1}\$\$ where \$0 \\le x \\le 1\$, \$\\alpha \> 0\$, and \$\\beta \> 0\$
- \$\\mu=E(X)=\\frac{\\alpha}{\\alpha+\\beta}\$
- \$\\sigma^2=Var(X)=\\frac{\\alpha\\beta}{(\\alpha+\\beta)^2(\\alpha+\\beta+1)}\$
- \$\\sigma=SD(X)=\\sqrt{\\frac{\\alpha\\beta}{(\\alpha+\\beta)^2(\\alpha+\\beta+1)}}\$ |
| Readable Markdown | This applet computes probabilities and percentiles for beta random variables: \$\$X \\sim Beta(\\alpha, \\beta)\$\$
#### Directions
- Enter the shape \$\\alpha\$ and the shape \$\\beta\$.
- To compute a left-tail probability, select \$P(X \\lt x)\$ from the drop-down box, enter a numeric \$x\$ value in the blue box and press "Enter" or "Tab" on your keyboard. The probability \$P(X \\lt x)\$ will appear in the pink box. Select \$P(X \\gt x)\$ from the drop-down box for a right-tail probability.
- To determine a percentile, enter the percentile (e.g. use 0.8 for the 80th percentile) in the pink box and select \$P(X \\lt x)\$ from the drop-down box and press "Tab" or "Enter" on your keyboard. The percentile \$x\$ will appear in the blue box.
On the graph, the \$x\$ value appears in blue while the probability is shaded in pink.
#### Details
- Probability density function \$\$f(x)=\\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} x^{\\alpha-1} (1-x)^{\\beta-1}\$\$ where \$0 \\le x \\le 1\$, \$\\alpha \> 0\$, and \$\\beta \> 0\$
- \$\\mu=E(X)=\\frac{\\alpha}{\\alpha+\\beta}\$
- \$\\sigma^2=Var(X)=\\frac{\\alpha\\beta}{(\\alpha+\\beta)^2(\\alpha+\\beta+1)}\$
- \$\\sigma=SD(X)=\\sqrt{\\frac{\\alpha\\beta}{(\\alpha+\\beta)^2(\\alpha+\\beta+1)}}\$ |
| Shard | 115 (laksa) |
| Root Hash | 15749649359141072315 |
| Unparsed URL | edu,uiowa!divms,homepage,/~mbognar/applets/beta.html s443 |