- #1

Charlotte87

- 21

- 0

## Homework Statement

Assume that X is squared-Chi-distributed, which means that the moment generating function is given by:

[itex]m(t)=(1-2t)^{-k/2}[/itex]

Use the mgf to find E(X) and var(X)

## The Attempt at a Solution

I know that m'(0)=E(X), and m''(0)=var(X).

So I find:

[itex]m'(t)=k(1-2t)^{-(k/2)-1}[/itex]

which gives m'(0)=k

Similarily, I find

[itex]m''(t)=(k^{2}+2k)(1-2t)^{-(k/2)-2}[/itex]

which gives m''(0)=k^2+2k

However, in my textbook, it says that the variance of a square-chi distribution should be 2k, not k^2. Where do I go wrong?