# Question

The number of cars approaching a toll booth in a minute follows a geometric random variable with a mean of 2 cars/ minute. The time it takes the toll collector to serve each car is an exponential random variable with a mean of 20 seconds.

(a) Find the mean time that the toll collector will require to serve cars that arrive in a one- minute interval.

(b) Find the PDF of the time that the toll collector will require to serve cars that arrive in a one- minute interval.

(c) What is the probability that the toll collector will require more than one minute to serve the cars that arrive during a one- minute interval, thereby causing a queue to form?

(a) Find the mean time that the toll collector will require to serve cars that arrive in a one- minute interval.

(b) Find the PDF of the time that the toll collector will require to serve cars that arrive in a one- minute interval.

(c) What is the probability that the toll collector will require more than one minute to serve the cars that arrive during a one- minute interval, thereby causing a queue to form?

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