Question: Let X ~ Uniform ([0, 1]). (a) (3 points) Compute the moment generating function of X. Be careful to distinguish when t = 0 or

Let X ~ Uniform ([0, 1]). (a) (3 points) Compute the moment generating function of X. Be careful to distinguish when t = 0 or t # 0. (b) (6 points) For each n E N, let Xn be a discrete random variable with PMF k PX =P( Xn = for k = 0, 1, ..., n. n n+1 Show that Xn converges in distribution to X as n - co. You may use, without proof, the fact that 1- ex lim = -1

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