Let X 1 , X 2 , , Xn be independent random variables with Xi Exponential().
Question:
Let X1, X2, ⋯, Xn be independent random variables with Xi ∼ Exponential(λ). Define Y = X1 +X2 +⋯+Xn.
As we will see later, Y has a Gamma distribution with parameters n and λ, i.e., Y ∼ Gamma(n,λ). Using this, show that if Y ∼ Gamma(n,λ), then EY = n/λ and V ar(Y ) = n/λ2.
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Related Book For
Introduction To Probability Statistics And Random Processes
ISBN: 9780990637202
1st Edition
Authors: Hossein Pishro-Nik
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