- #1

EthanW

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I am trying to get the hang of Probability Generating Functions, but I don't quite understand them fully.

For example, I've got the PGF of a random variable X, called H:

[tex]H(s) = \frac{1}{3}\cdot(1+s+s^2)[/tex]

Now, then there is a random variable Y, with Y = X + 1, and I want to solve the PGF of Y I do:

[tex]G_Y(s) = G_{x+1}(s) = E[s^{x+1}] = E[s^x]\cdot E

I don't know how to go further at this point, can someone point me in the right direction?

Thanks.