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Limit Moment-Generating Functions

Let S^2 be the sample variance of a random sample of size n from N (mean, standard deviation). Show that the limit, as n -> infinity , of the moment -generating function of e^sigma2t. Thus, in the
limit, the distribution of S^2 is degenerate with probability 1 at sigma^2 . (See attached file for full problem description with proper symbols)

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Solution Summary

This solution applies concepts calculus to the limit function to show that with n -> infinity the distribution of s^2 is degenerate with probability 1 at sigma^2 (variance). All steps are shown with explanations and calculations.

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