If the moment-generating function of a random variable W

Chapter 3, Problem 9E

(choose chapter or problem)

Get Unlimited 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.

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


Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back