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

 

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Let (Yn)nEN be i.i.d. random variables with Yı ~ N(0,1). Denote by An the sample mean of the squares of these variables: n 1 Y? ΣΥ An i=1 Define a sequence of random variables (Bn)nẸN 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? Let (Yn)nEN be i.i.d. random variables with Yı ~ N(0,1). Denote by An the sample mean of the squares of these variables: n 1 Y? ΣΥ An i=1 Define a sequence of random variables (Bn)nẸN 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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