Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of
Chapter 5, Problem 5.2-7(choose chapter or problem)
Let \(X_{1}\) and \(X_{2}\) be independent chi-square random variables with \(r_{1}\) and \(r_{2}\) degrees of freedom, respectively. Show that
(a) \(U=X_{1} /\left(X_{1}+X_{2}\right)\) has a beta distribution with \(\alpha=r_{1} / 2\) and \(\beta=r_{2} / 2\).
(b) \(V=X_{2} /\left(X_{1}+X_{2}\right)\) has a beta distribution with \(\alpha=r_{2} / 2\) and \(\beta=r_{1} / 2\).
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