random signals question

| January 14, 2016

A statistician wants to estimate the mean height h (in meters) of a population, based on n independent samples X1, middot middot middot , Xn, choose uniformly from the entire population. He uses the sample mean Mn = (X1 + X2 + …, Xn)/n as the estimate of h. We also assume that he knows Var(Xi) = 0.5 (meter2).How large should n be so that the variance of Mn is at most 10-4.Please use the weak law of large numbers, i.e., to answer that how large n should be so that the estimate is within 0.05 meter from h, with probability at least 0.9?

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