# moment generating function of a binomial random variable

• Mar 20th 2012, 03:39 PM
Jeonsah
moment generating function of a binomial random variable
Hey guys, I am trying to wrap my head around this problem. I understand everything except how they get to a certain point. Here is the problem:

Derive the moment generating function of a binomial random variable and then use your result to verify the formulas for the mean and variance given in the text.

the books solution:

http://i909.photobucket.com/albums/a.../problem-1.jpg

The red arrow in the picture is where I am lost. I can not figure out how they got from the left side of the arrow to the right. Can someone help me out?

Thanks
• Mar 24th 2012, 10:06 AM
thm43608
Re: moment generating function of a binomial random variable
Use the binomial theorem with $a=pe^t$ and $b=1-p$.

You should be able to figure it out from there.