(Iterated Expectation) Suppose X1 U 0,1 and, for n ge 2 X n given that X n 1 x is distributed as U 0,x What is E(X n ) and its limit as n rarr infin

Question: (Iterated Expectation). Suppose X1 ~ U[0,1] and, for n ≥ 2; X_{n} given that X_{n-1} = x is distributed as U[0,x]. What is E(X_{n}) and

(Iterated Expectation). Suppose X1 ~ U[0,1] and, for n ≥ 2; X_{n} given that X_{n-1} = x is distributed as U[0,x]. What is E(X_{n}) and its limit as n →∞?

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