# Moment generating function

• Apr 10th 2008, 03:02 PM
MatsSundin
Moment generating function
Let Y be a Standard Normal random variable.
What is the moment generating function of Y^2?
What is the distribution of Y^2?
Find V(2*(Y^2) + 3)
any help would be appreciated
• Apr 10th 2008, 05:45 PM
mr fantastic
Quote:

Originally Posted by MatsSundin
Let Y be a Standard Normal random variable.
What is the moment generating function of Y^2?
What is the distribution of Y^2?
Find V(2*(Y^2) + 3)
any help would be appreciated

Post #7 of this thread: http://www.mathhelpforum.com/math-he...tml#post119542

derives the distribution of Y^2 (the notation is different of course).

Y^2 follows a chi-square distribution of degree 1. You can either look up the moment generating function or derive it from the definition.

Standard theorem: Var(aZ + b) = a^2 Var(Z). So Var(2Y^2 + 3) = 4 Var(Y^2).

To get Var(Y^2) you can either look it up or derive it from E[(Y^2)^2] - (E[Y^2])^2. The required expectations can be got from the moment generating function of Y^2.
• Apr 10th 2008, 07:16 PM
mathlete2
Are you Sure?
But Chi square is a only for gamma distributed random variables and not for standard random variables. So this couldn't work? Correct?
• Apr 10th 2008, 07:20 PM
mr fantastic
Quote:

Originally Posted by mathlete2
But Chi square is a only for gamma distributed random variables and not for standard random variables. So this couldn't work? Correct?

If Y is normal then Y^2 is chi-squared. The chi-squared disribution is a special case of the gamma distribution. Read Chi-Squared Distribution -- from Wolfram MathWorld.