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 :

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