Question: Let (Yn)nEN be i.i.d. random variables with Y ~ N(0,1). Denote by An the sample mean of the squares of these variables: n 1

Let (Yn)nen be i.i.d. random variables with Y1 ~ N(0,1). Denote by An the sample mean of thesquares of these variables:1ΣΥ

Let (Yn)nEN be i.i.d. random variables with Y ~ N(0,1). Denote by An the sample mean of the squares of these variables: n 1 Y? An i=1 Define a sequence of random variables (Bn)nN by Bn := eAn for all n e N. a) Does the sequence Bn converge in probability to a constant b? If yes, what is b? b) Does the sequence Bn converge in distribution to a constant b? If yes, what is b?

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