Advanced Statistics Problems

3. rotational invariance and correlation: Y~ unif(B”) and U~ unif (S-1) a) With X; = U?, determine EX1, 0(X1) and p(X1, X2). (10) b) With V; = Y/?, determine EV1, o(Vi) and p(V1, V2). (10) 5. order statistics with the standard exponential: 21, …, Zn IID Z ~ exp (1), neN a) With Zo=0, determine the joint distribution of the coverages, Zo) -Z(i-1), i = 1,…, n. (12) b) Using the result in a), or otherwise, obtain EZ(i) and o(Zn)) for every 1

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