Solution Found!
Use the moment-generating function of a gamma distribution
Chapter 3, Problem 10E(choose chapter or problem)
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) ]