Let me ask a more basic question first.

one of the examples in the book states let the moments of X be defined by E(X^r) = 0.8, r = 1,2,3...

then goes on to find the MGF.

and that P(X=0) = 0.2 and P(X=1) = 0.8.

What is r? If it was just E(X) = 0.8, then the expected value of the random variable X is 0.8. but what is the expected value of a random variable raised to a variable power??

and if E(X^r) = a constant is a bernoulli distribution, is there some similar association I can make for E(X^r) = Constant^r?

edit: just realized/rememberd/associated the notation E(X) finds the first moment, and E(X^2) finds the second etc. so 5^1 is the first moment and 5^2 is the second etc.