Question

3.25. Suppose45%ofthecarsontheroadaredomesticbrandsand55%areforeign brands. Let N.t/ be the number of cars crossing at a given toll booth during .0;t?. Suppose fN.t/;t ? 0g is a PP with rate 40 per minute.

(1)What is the probability that four foreign cars and five domestic cars cross the intersection during a 10-second interval?

(2)In Computational Problem 3.25, suppose 30 foreign cars have crossed the toll booth during a 1-minute interval. What is the expected number of domestic cars that cross the intersection during this interval given this information?

(3)Consider the toll booth of Computational Problem 3.25. Suppose the toll paid by a car at the toll booth is $1.00 with probability .3 and $2.00 with probability .7. What are the mean and variance of the toll collected at the toll booth during 1 hour?

Answer 1