Question: Let X1,X2, . . . be independent, identically distributed random variables with E[X] = 2 and var(X)=9, and let Yi = Xi/2i. We also define

Let X1,X2, . . . be independent, identically distributed random variables with E[X] = 2 and var(X)=9, and let Yi = Xi/2i.

We also define Tn and An to be the sum and the sample mean, respectively, of the random variables Y1, . . . , Yn.

(a) Evaluate the mean and variance of Yn, Tn, and An.

(b) Does Yn converge in probability? If so, to what value?

(c) Does Tn converge in probability? If so, to what value?

(d) Does An converge in probability? If so, to what value?

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