Use the moment-generating function of a gamma distribution to show that E(X) = and

Chapter 3, Problem 3.2-10

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QUESTION:

Use the moment-generating function of a gamma distribution to show that \(E(X) = \alpha \theta\) and \(\text{Var}(X) = \alpha \theta^2\).

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QUESTION:

Use the moment-generating function of a gamma distribution to show that \(E(X) = \alpha \theta\) and \(\text{Var}(X) = \alpha \theta^2\).

ANSWER:

Step 1 of 5

The moment-generating function of a gamma distribution is given below.

The first derivative of the MGF of gamma distribution is:

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