Let X1, , Xn, be an i.i.d. sample from an exponential distribution with the density function

a Find the mle of .

b What is the exact sampling distribution of the mie?

c Use the central limit theorem to find a normal approximation to the sampling distribution.

d Show that the mie is unbiased, and find its exact variance. (Hint: The sum of the Xi follows a gamma distribution.)

e Is there any other unbiased estimate with smaller variance?

f Find the form of an approximate confidence interval for .

g Find the form of an exact confidence interval for r.

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