Let {X} be a sequence of mutually independent random variables such that X = 1 with probability

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Let {X} be a sequence of mutually independent random variables such that X = 1 with probability (1-2)/2 and X = 2" with prob- ability 21.

Prove that both the weak and the strong law of large numbers apply to (X). [Note: This shows that the condition (5.5) is not necessary.]

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