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with the60. Let Xi,.... X, be andensity functioniid. sample from an exponential distribution0

Question
with the
60. Let Xi,.... X, be an
density function
iid. sample from an exponential distribution
0<x<00
a. Find the mle of τ
b. What is the exact sampling distribution of the mle?
c. Use the central limit theorem to find a normal approximation to the sampling
distribution.
d. Show that the mle is unbiased, and find its exact variance. (Hint: The sum of
the X, 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 t.
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with the 60. Let Xi,.... X, be an density function iid. sample from an exponential distribution 0<x<00 a. Find the mle of τ b. What is the exact sampling distribution of the mle? c. Use the central limit theorem to find a normal approximation to the sampling distribution. d. Show that the mle is unbiased, and find its exact variance. (Hint: The sum of the X, 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 t.

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Step 1

Hey, since there is multiple subpart questions posted, we will answer first three subparts. If you want any specific subpart to be answered then please submit that subpart only or specify the subpart number in your message.

Step 2

a. Computing mle of τ:

The mle estimate of a parameter is that value of the parameter which maximizes the likelihood function.

The mle of τ is given below:

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Step 3

The mle estimate of τ is ...

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