Moment Generating Function

alabama14

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Oct 30, 2011
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Let Y be a random variable following a negative binomial distribution with parameters r and p. It is known that the moment generating function of this random variable is

M(t) = ((pe^t)/(1-(1-p)e^t))^r

Use M(t) to find E(Y) and V(Y).

Am I supposed to find the first derivative of M(t) to get E(Y)? But then what about V(Y)? I know for negative binomial distributions, E(X) = rq/p and V(X) = rq/p^2, but I don't know if I need to use that for this problem.
 
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