Let X have a beta distribution with parameters ? and ?.
Chapter 5, Problem 8E(choose chapter or problem)
Let \(X\) have a beta distribution with parameters \(\alpha\) and \(\beta\). (See Example 5.2-3.)
(a) Show that the mean and variance of \(X\) are, respectively,
\(\mu=\frac{\alpha}{\alpha+\beta} \quad \text { and } \quad \sigma^{2}=\frac{\alpha \beta}{(\alpha+\beta+1)(\alpha+\beta)^{2}}\) .
(b) Show that when \(\alpha>1\) and \(\beta>1\), the mode is at \(x=(\alpha-1) /(\alpha+\beta-2)\).
Equation Transcription:
Text Transcription:
X
Alpha
Beta
mu =alpha/alpha + beta
sigma^2= alpha beta /(alpha + beta +1)(alpha+ beta)^2
alpha>1
Beta >1
x=(alpha-1)/(beta+-2)
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