3. Let Y1, . . . , Yn ~ i.i.d. random variables from the following distribution:
f ( y | ? ) = ? y?-1 for 0 < y < 1; ? > 0
A. Write down the likelihood L(?).
B. Find the Method of Moments estimate for ?.
C. Find the Maximum Likelihood Estimate for ?.
D. How does the MOM depend on the data? (What is the function of the data that appears in the MOM?) Similarly, how does the MLE depend on the data? Do you expect these two estimators to give the same estimate for ? in a given sample from the density f ( y | ? ). Explain.
E. Use R to graph the likelihood as a function of theta.
