Let (X_{1}, X_{2}, ldots, X_{5}) be 5 independent random variables. Find the moment generating function [M_{sum X_{i}}(t)=Eleft(e^{tleft(X_{1}+X_{2}+cdots+X_{5}
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Let \(X_{1}, X_{2}, \ldots, X_{5}\) be 5 independent random variables. Find the moment generating function
\[M_{\sum X_{i}}(t)=E\left(e^{t\left(X_{1}+X_{2}+\cdots+X_{5}\right)}\right)\]
of the sum when \(X_{i}\) has a gamma distribution with \(\alpha_{i}=2 i\) and \(\beta_{i}=2\).
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SOLUTION Since the random variables X1 X2 X5 are independe...View the full answer
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Related Book For 
Probability And Statistics For Engineers
ISBN: 9780134435688
9th Global Edition
Authors: Richard Johnson, Irwin Miller, John Freund
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