Suppose X1, X2, . . . , Xn are i.i.d. Exp(µ) with the density f(x) =...

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Question

Suppose X1, X2, . . . , Xn are i.i.d. Exp(µ) with the density f(x) = $1-μ$ for x>0

(a) Use method of moments to find estimators for µ and µ^2 .

(b) What is the log likelihood as a function of µ after observing X1 = x1, . . . , Xn = xn?

(c) Find the MLEs for µ and µ^2 . Are they the same as those you find in part (a)?

(d) According to the Central Limit Theorem, what is the approximate distribution for $\overline{X}$ when n is large?

(e) Suppose that $\overline{x}$ = 5.34 for a random sample of size 64, determine the approximate 95% confidence interval for µ?

Please show as many steps as possible because I am struggling with this class right now and I am not understanding the estimation methods very well. PLEASE HELP ME!

math Statistics-And-Probability

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