If X1,X2,...,Xn are independent random variables having
Chapter 9, Problem 8.57(choose chapter or problem)
If \(X_1\), \(X_2\), . . . , \(X_n\) are independent random variables having identical exponential distributions with parameter \(\theta\), show that the density function of the random variable \(Y = X_1 + X_2 +· · ·+ X_n\) is that of a gamma distribution with parameters \(\alpha = n\) and \(\beta = \theta\).
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