1. Let X1,...Xn be a sequence of independent random variables from a distribution Fe depending on an unknown parameter 0 € R. Let ô, be an estimator of 0 of the form n i=1 where Y; = g(X;) for some known function g. Assume that, for each i = 1, ..., n, the mean of Y; is 0 and the variance is finite. For a given sample x1,..., 500 of size n = 500, we find that O500 Ussing this information, construct an approximate 95%-confidence interval for 0. = 2 and estimate the variance of 0500 by 0.3.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.