X1 xnnbspare independent uniform random variables all with, Basic Statistics

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X1 xnnbspare independent uniform random variables all with

X₁,..., X_n are independent uniform random variables, all with expected value µ_X = 7 and variance Var[X] = 3.

(a) What is the PDF of X₁?

(b) What is Var[M₁₆(X)], the variance of the sample mean based on 16 trials?

(d) Would you expect P[M₁₆(X) > 9] to be bigger or smaller than P[X₁ > 9]? To check your intuition, use the central limit theorem to estimate P[M₁₆(X) > 9].

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