Question: Let X be a discrete random variable with probability mass function P(X = 6) = 4/9 , P(X = 2) = 1/9 , P(X =

Let X be a discrete random variable with probability mass function P(X = 6) = 4/9 , P(X = 2) = 1/9 , P(X = 0) = 2/9 , P(X = 3) = 2/9

a) Find the moment generating function (MGF) of X.

b) Find the mean of X by differentiating the MGF to find the first moment, E[X].

c) Find the second moment of X, E[X2 ], and then find the variance of X, V (X)

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