Let Xi be a random variable from a uniform distribution on the interval [0,b]. Thus the lower bound is known but not the upper b
ound. You observe n many independent and identically distributed Xi ’s. What is the expected value of the sample mean X¯ = 1 n Pn i=1 Xi? How could you transform X¯ to make it an unbiased estimator of b (that is to say the expectation of the estimator is equal to b)
