Let X1, X2, ... , Xn be a random sample from N(, 2), where 2 is known. (a) Show that Y = (X1 + X2)/2 is an unbiased estimator of . (b) Find the RaoCramr lower bound for the variance of an unbiased estimator of for a general n. (c) What is the efficiency of Y in part (a)?

Lecture 9/25/2017 → Chapter 3: Probability ← SECTION 3.1 Probability: A number between 0 and 1 representing how likely it is that an event will occur. Random Experiment: An experiment whose outcome is not known until it is observed. Sample Space (S): a set of outcomes of a random experiment. Every possible outcome must be listed once and only once. Sample Point: An element of the sample space. Event: A subset of the sample space. That is, any collection of outcomes forms an event. EVENTS, like sets, are represented using capital letters: A, B, etc. Experiment: Toss a coin twice and observe the result. o Sample Space: S = {HH, HT, TH, TT} o An example of a sample point is: HT. o Let A be the event that there is exactl