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19 days ago
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Age cutoffPASSdownload_stamp > now() - 6 MONTH0.7 months ago
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Page Details

PropertyValue
URLhttps://homepage.divms.uiowa.edu/~mbognar/applets/beta.html
Last Crawled2026-03-30 13:03:28 (19 days ago)
First Indexed2018-06-20 20:14:25 (7 years ago)
HTTP Status Code200
Meta TitleBeta Distribution Applet/Calculator
Meta Descriptionnull
Meta Canonicalnull
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)}}\$
Shard115 (laksa)
Root Hash15749649359141072315
Unparsed URLedu,uiowa!divms,homepage,/~mbognar/applets/beta.html s443