Determine distribution given moment generating function


New Member
I am given two moment generating functions, and need to calculate some probabilities regarding them.

The first is: M(t) = [math]((2/3)e^t + (1/3))^3[/math]

I recognized this to be a binomial distribution with n = 3 and p = 2/3

The second is: M(t) = [math](1/3) + (1/6)e^{6t} + (1/2)e^{2t}[/math]

I am having trouble figuring out what distribution this follows (is it also a binomial distribution, just not simplified? If so, how would one simplify it?)

Any help would be greatly appreciated!