Suppose X has an exponential distribution with a mean of 10

Suppose X has an exponential distribution with a mean of 10. Calculate P(X < 15|X > 10). (Hint: apply the memoryless property)

Solution

Note that

P(X < 15|X > 10) = P(10<x<15) / P(x>10)

= [(1-e^(-15/10)) - (1 - e^(-10/10))] / [e^(-10/10)]

= 0.39346934 [ANSWER]