Let X1, . . . , Xn be a random sample from a uniform(1, 2) distribution.

1.Find the MLEs of 1 and 2.

2.Find a sufficient statistic for 1, assuming that 2 is known

3.Now let = 2 = 1 and thus the random sample is from a uniform(, ). Find a constant c such that T = c X(n) X(1) is an unbiased estimator of parameter .

Note: E(X(1)) is given: E(X(1)) = ((1n))/ (n+1) .