Problem 2; Sampling Distributions #8: Assume the following theorem: If R.V.'s X1,X2,..., Xn are such that the P(X > M) 0 and lim0 V(Y = lim0 V(-1 Xk) oo), then the distribution of the standardized...

Extracted text: Problem 2; Sampling Distributions #8: Assume the following theorem: If R.V.'s X1,X2,..., Xn are such that the P(X > M) 0 and lim0 V(Y = lim0 V(-1 Xk) oo), then the distribution of the standardized mean of Xi approaches the stan- dard normal distribution. Now, consider the sequence of independent random variables (Xk)1, and assume each has uniform density independent and uniformly bounded (i.e. 3M > 0 1 1 0 xk2 k fr(k) 2 k 0 otherwise Use the theorem to show that the central limit theorem holds.