Motor vehicles arrive at a toll gate according to a Poisson process with rate A : 2 vehicles per minute The vehicles arriving at the gate belong to classes 1, 2 or 3 with probabilities 1/2, 1/3 or 1/5 , respectively. The drivers pay tolls of $1 , $2 or $5 depending on the classes 11 2, or 3 their vehicles belong to. 1. Find the probability that exactly $1 is collected in a period of 2 minutes. 2. Find the probability that the first toll collected is $1. 3. Find the probability that the waiting time between two vehicles that pay $5 is more than 10 minutes. 4. Find the mean and the variance of the amount in dollars collected in any given hour