Question: =+ (a) Prove there is a subsequence {X ,, ) and a random variable X such that lim , X =X with probability 1. Hint:

(a) Prove there is a subsequence {X ,, ) and a random variable X such that lim , X„ =X with probability 1. Hint: Choose increasing n, such that P[!X„ ,, - X„|>2 ~* ]<2 ~* for m, n ≥n ,. Analyze P[|X ,, ., - X„ ,, |>2 ~* ].

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