Suppose that buses arrive are scheduled to arrive at a bus stop at noon but are always X minutes late, where X is an exponential random variable with probability density function fX(x) = λe−λx. Suppose that you arrive at the bus stop precisely at noon. (a) Compute the probability that you have to wait for more than five minutes for the bus to arrive. (b) Suppose that you have already waiting for 10 minutes. Compute the probability that you have to wait an additional five minutes or more.

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Suppose that buses arrive are scheduled to arrive at a bus stop at noon but are
always X minutes late, where X is an exponential random variable with probability density
function fX(x) = λe−λx. Suppose that you arrive at the bus stop precisely at noon.
(a) Compute the probability that you have to wait for more than five minutes for the bus
to arrive.
(b) Suppose that you have already waiting for 10 minutes. Compute the probability that
you have to wait an additional five minutes or more.

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