Use the moment-generating function of a gamma distribution

Chapter 3, Problem 10E

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QUESTION:

Problem 10E

Use the moment-generating function of a gamma distribution to show that E(X) = αθ and Var(X) = αθ2.

Questions & Answers

QUESTION:

Problem 10E

Use the moment-generating function of a gamma distribution to show that E(X) = αθ and Var(X) = αθ2.

ANSWER:

Answer :

Step 1 of 3 :

We have to show that the E(x) =  and Var(x) =

We know that,the moment generating function of X is

M(t) =

M(t) =

Differentiate the moment generating function

(t) = []

            = - (1 - )

            = -  (-)

          =

Then, (t) = [ (t) ]

                       =  [ -(+1) (-) ]

                      =  [ (+1) ]


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