Moment generating function of the negative binomial distribution.
I am trying to find the moment generating function for the negative binomianl distribution. I know that it's baiscly finding <e^ty>. I therefore put e^ty into the sum from y=0 to infinity. I tried a few ways of solving it but I am stuck for quite sime time now. Here is what I tried:
- Expanding e^ty and use it's summation form. But this only led to showing how the moment generating function works.
- Use different substitutions to try and get the original form or one of it's varience back with a factor outside the summation. But this is not working too.
Am I going in the right direction?