Question: Prove that for the distribution function of any random variable, limx F(x) = 1. Hint: Use the result of Exercise 4.1.13 and the theorem from

Prove that for the distribution function of any random variable, limx→∞ F(x) = 1. Hint: Use the result of Exercise 4.1.13 and the theorem from real analysis that if limn→∞ F(xn) = L for every sequence xn increasing to ∞, then limx→∞ F(x) = L.

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