Let X = {X i = 1,...,n} be a random sample from the Normal distribution where...

 

Transcribed Image Text:

Let X = {X i = 1,...,n} be a random sample from the Normal distribution where X~ N(u, 1) and assume that you estimate parameter p using the sample average X (which is N (,)-distributed). From three different samples, you obtain the following estimates = 1,2 = 3, and 3 = 5. 1. Calculate the absolute loss for each of the three p estimates. 2. Calculate the risk of the estimator given absolute loss. Hint: f(x) dx = f f (x) dx + f(x) dx. Hint: The symmetry of the normal distribution as well as substituting - during the integration will be helpful. Let X = {X i = 1,...,n} be a random sample from the Normal distribution where X~ N(u, 1) and assume that you estimate parameter p using the sample average X (which is N (,)-distributed). From three different samples, you obtain the following estimates = 1,2 = 3, and 3 = 5. 1. Calculate the absolute loss for each of the three p estimates. 2. Calculate the risk of the estimator given absolute loss. Hint: f(x) dx = f f (x) dx + f(x) dx. Hint: The symmetry of the normal distribution as well as substituting - during the integration will be helpful.