2. The number of accidents at an intersection is a Poisson process



N(t) : t ≥ 0

with rate 2.3 per week. Let Xi be the number of injuries in accident i. Suppose that {Xi} is a sequence of independent and identically distributed random variables with mean 1.2 and standard deviation 0.7. Furthermore, suppose that the number of injuries in each accident is independent of the number of accidents that occur at the intersection. P Let Y (t) = N(t)

i=1 Xi; then Y (t), the total number of injuries from the accidents at that intersection, at or prior to t, is said to be a compound Poisson process. Find the expected value and the standard deviation of Y (52), the total number of injuries in a year.