A two-way street (i.e. vehicles pass from left and right). The number of cars coming from the left side follows a Poisson distribution with = 20 cars per minute, and the number of cars coming from the right side follows a Poisson distribution with =30 cars per minute. These two passion events are independent. A person wants to pass that street, so he waits until no cars will come by in the next T = 12 seconds from both sides. Let U be the time the person waits before starting to cross.

a) What is the expected value of U?

b) Suppose the number of cars coming from the left is a passion with =20 per minute, and the number of Fire engines coming from the right follow passion with =10 per minute. A person wants to pass that street, so he waits until no car from the left in T=10 seconds and no Fire engines from the right in T=20 seconds. What is his expected waiting time?