Example
Example 5.2 Suppose that the amount of time one spends in a bank is 1 . What is the exponentially distributed with mean ten minutes, that is, λ = 10 probability that a customer will spend more than fifteen minutes in the bank? What is the probability that a customer will spend more than fifteen minutes in the bank given that she is still in the bank after ten minutes? Solution: If X represents the amount of time that the customer spends in the bank, then the first probability is just P{X > 15} = e−15λ = e−3/2 ≈ 0.220