Let us say that there is a distribution as written below

f(y|)=(+1)y^() ; 0-1

a. Determine the MLE of from a random sample of size n.

b. Compute the distribution of the MLE (You can start by looking into the Inverse Gamma distribution).

c. Use the distribution you found in part b to determine the mean and variance of the MLE.

d. Is the MLE unbiased? If yes, say so and continue to part e. If not, propose an unbiased estimator.

e. What is the variance of the unbiased estimator that you ended up with in part d?

f. Is the unbiased estimator from part d consistent for ?

g. Is the MLE of sufficient for ? What does that say about the estimator from part d?

h. Determine the MoME for .

Please show all of your work! Thank you!