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2. A moment generating function (a) (5 pts) Suppose a random variable X has the moment generating function Mx(t) : = E[etx]. Let g(t) :=

2. A moment generating function (a) (5 pts) Suppose a random variable X has the moment generating function Mx(t) : = E[etx]. Let g(t) := log Mx(t), then prove that g"(0) = Var[X]. (b) (5 pts) Suppose a random variable Y has the following moment generating function est My (t) = 1 - 4t2 . Find E[Y] and Var[Y]

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