# Question: Let F x be the cdf of the continuous type random variable

Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x) = 0 for x ≤ 0 and 0 < F(x) < 1 for 0 < x. Prove that if

P(X > x + y | X > x) = P(X > y),

Then

F(x) = 1 − e−λx, 0 < x.

Which implies that g(x) = acx.

P(X > x + y | X > x) = P(X > y),

Then

F(x) = 1 − e−λx, 0 < x.

Which implies that g(x) = acx.

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