Q1: a) Suppose a random sample of size n is taken from a normal distribution with mean u and variance o, where o is known. Compare the Cramer –Rao Lower bound with the variance û = ỹ = -Ey, Examine whether F is an efficient estimator for µ. b) Let Y, .,Y, be a random sample from a uniform distribution on (0, 0). The estimator ô = (n +1)Y, is unbiased estimator for 0. Prove or disprove the estimator ô, is consistent for 0

A machine puts golf balls into boxes and then loads the boxes into cases. The machine is normally able to load 25 cases of golf balls per hour. There are 20 boxes in one case. There are 12 balls in one box. Today, the machine is running a little faster than usual so that it takes 0.2 seconds less time to load one golf ball into a box than it normally does. What is the machine's new rate in cases of golf balls per hour!

Suppose that the local newspaper reported that Millerville and Big Lake both had 50 murders last year. However, 5 years ago, Millersville had 42 murders and Big Lake had just 29. Calculate the absolute change and the perchance for each city over the five years. Could the newspaper make the claim that crime had gone up by the same amount in each city? Explain

Find $ such that D =F. x - hg - hp-