1. Let Y, t e N, be a sequence of independent, identically distributed ran- dom variables on a given probability space (

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1 Let Y T E N Be A Sequence Of Independent Identically Distributed Ran Dom Variables On A Given Probability Space 1 (27.2 KiB) Viewed 49 times

1. Let Y, t e N, be a sequence of independent, identically distributed ran- dom variables on a given probability space (12, F, P) such that E(Y) = 0 and Var(Y) = 1. (i) Define X] :=Y, and for t > 2 X :=Y1-1+Y. Compute E(Xi) and Cov(X2, Xx-x) for t e N and for s = 0, 1, 2,...,t - 1. (30 Marks) (ii) Define 2 = Y, and 2:= 24-1+Y. > 2. Prove that for arbitrarily fixed t e N and all s = 0,1,2,....t-1 E(Z) = 0, and Cov(Z1, Z-s) = t-s