Suppose that Xn converges weakly to X, and X = a almost surely. Prove that Xn...

 

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Suppose that Xn converges weakly to X, and X = a almost surely. Prove that Xn converges to X in probability. [Hint: From the Portmanteau Lemma, it is known that Xn converges weakly to X if and only if E[(X)] E[f(x)] for all bounded and continuous function f.] Suppose that Xn converges weakly to X, and X = a almost surely. Prove that Xn converges to X in probability. [Hint: From the Portmanteau Lemma, it is known that Xn converges weakly to X if and only if E[(X)] E[f(x)] for all bounded and continuous function f.]

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To prove that Xn converges to X in probability well use the definition of conve... View the full answer