For an F-distribution, find f0.05,8,15, f0.01,14,19, and f0.99,15,7

Given is a random sample X1, X2, . . . , Xn from a Bernoulli distribution with parameter p. One considers the estimators T1 =1/n(X1 + + Xn) and T2 = min{X1, ..., Xn} of p.(a) Calculate the bias of T1 and of T2.(b) Calculate MSE(T1) and MSE(T2).(c) Which estimator would you prefer when n = 2?

Two different machines process work at the same mean rate . However machine 1 is newer than machine 2 and therefore has a smaller variability. We know that variance of the rate for machine 1 is 21, and that the variance of the rate for machine 2 is 22 = a21. Suppose we have a random sample of size n1 of rates from machine 1 and a random sample of size n2 of rates from machine 2.(a) Show that X1 + (1 )X2 is an unbiased estimator for for each value of [0, 1].(b) Find the variance of these estimator as a function of .(c) What value of would minimize the MSE?