Let X be a random variable, and {Xn}1 a sequence of random variables, on a probability space (N,F,P). (a) Define what it means for the sequence of random variables {X} to converge to X in probability? nfn=1 (b) Define what it means for the sequence of random variables {X₂} to converge to X almost surely (a.s.)? (c) Prove that if {Xn}1 converges to X a.s. then {Xn} converges to X in prob- ability.

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