Solution Found!
If the moment-generating function of a random variable W
Chapter 3, Problem 9E(choose chapter or problem)
QUESTION:
Problem 9E
If the moment-generating function of a random variable W is
M ( t ) = (1 − 7t )−20,
find the pdf, mean, and variance of W.
Questions & Answers
QUESTION:
Problem 9E
If the moment-generating function of a random variable W is
M ( t ) = (1 − 7t )−20,
find the pdf, mean, and variance of W.
ANSWER:
Answer :
Step 1 of 2 :
Given,
The moment-generating function of a random variable W is M(t) = (1 - 7t.
The claim is to find the pdf, mean and variance of W
We know that the moment generating function of X is
M(t) =
=
Where, = 7 and = 20
The probability density function of gamma distribution is
f(x) = , x0
f(x) = , x0
f(x) = , x0