Let X i be i.i.d. Uniform(0, 1). We define the sample mean as a. Find E[M n

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Let Xi be i.i.d. Uniform(0, 1). We define the sample mean asMn X + X+...+Xn n

a. Find E[Mn] and Var(Mn) as a function of n.

b. Using Chebyshev's inequality, find an upper bound onP (M - 100) Mn 2

c. Using your bound, show thatP (M - 2 / 100) lim P n = 0.

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