Question: 18. Prove that if X is a positive, continuous, memoryless random variable with distribution function F, then F(t) = 1 et for some

18. Prove that if X is a positive, continuous, memoryless random variable with distribution function F, then F(t) = 1 − e−λt for some λ > 0. This shows that the exponential is the only distribution on (0,∞) with the memoryless property.

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