Question: Problem 1: The following numbers are 10 observations randomly sampled from the final-exam score distribution F, of which the mean and variance 2 are both

Problem 1: The following numbers are 10 observations randomly sampled from the final-exam score distribution F, of which the mean and variance 2 are both unknown. (a) (6pts) Now we would like to use the sample mean X=101i=110Xi to make inference about , please calculate the bootstrap estimation of Var(X). (Note: Give me the exact answer, do not estimate the answer by simulation.) (b) (8pts) Suppose the moment method is used to construct the estimator for 2 : ^2=101i=110(XiX)2 It is easy to show that for any distribution F,E(^2)=1092, which is a biased estimator of 2. Clearly describe how to estimate MSE(^2) by using 100 bootstrap samples. Also obtain this bootstrap estimate by simulation

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