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Use the moment-generating function of a gamma distribution to show that E(X) = and
Chapter 3, Problem 3.2-10(choose chapter or problem)
QUESTION:
Use the moment-generating function of a gamma distribution to show that \(E(X) = \alpha \theta\) and \(\text{Var}(X) = \alpha \theta^2\).
Questions & Answers
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: