(a) If the random variable Y has pdf f(y) then the pdf of is found as follows:

The cdf of is .

Since is the minimum of it follows that the event occurs if and only if the events occur for . Since the are independent and it follows that

.

The pdf of is given by : .

Now you have to calculate and see if it's equal to .

--------------------------------------------------------------------------------

(b) Calculate the expected value of the estimator and see whether or not you get .