A passenger and a bus arrive at the bus stop uniformly at ra

A passenger and a bus arrive at the bus stop uniformly at random between noon and 1pm.

a). what is the expected time the passenger waits for the bus? (The passenger only waits if he arrives first!)

b). Compute the probability that the passenger waits less than 15 min.

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Solution

a) Let X be a random variabledenoting the time the passenger waits for the bus.

X~U(0,60)

The expected time the passenger waits for the bus=E(X)=60/2=30

b) the probability that the passenger waits less than 15 min=P(X<15)=15/60=1/4