1 Problem 14 13 Let X1, ,Xn be independent random variables each having a gamma density with the same scale parameter Denote by i the shape parameter of the gamma density of the Xi Verify that X1 Xn has a gamma density with shape parameter 1 n and scale parameter

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Question: 1. Problem 14.13 Let X1,...,Xn be independent random variables each having a gamma density with the same scale parameter . Denote by i the shape

1. Problem 14.13 Let X1,...,Xn be independent random variables each having a gamma density with the same scale parameter β. Denote by αi the shape parameter of the gamma density of the Xi. Verify that X1 +···+Xn has a gamma density with shape parameter α1 +···+αn and scale parameter β.

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