Show that the density function of the random variable Y = X 1 + X 2 + ... + X n has gamma distribution with parameters α = n and β = θ , if X 1 , X 2 , ... , X n are independent random variables having identical exponential distributions with parameter θ .

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Chapter 8.8, Problem 57RE

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Show that the density function of the random variable Y=X1+X2+...+Xn has gamma distribution with parameters α=n and β=θ, if X1,X2,...,Xn are independent random variables having identical exponential distributions with parameter θ.

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