Homework 5 Due Nov 8, 2011 Ch 6: 20 ; Ch 7: 4, 15; Ch8: 34, 46 1. Let X ∼ Poisson ( β ). Find the bias, variance and MSE of ¯ X as well as ∑ X i N-1 . Using the CLT, what is the asymptotic distribution of ¯ X . 2. Assume X ∼ N ( μ,σ 2 ). Use the CLT to derive asymptotic conﬁdence intervals for σ 2 , using S 2 . Use the data from question 34 to compute a conﬁdence interval and compare it to you answer from question 46. Discuss why there are or are not diﬀerence between the two approaches
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