1. Customers arrive to the store according a Poisson process with intensity = 1customers per hour. Let N[0, t] be the number of arrivals between [0, t].

(a) Find the probabilityP(N[0, 2] = 2, N[2, 3] = 1|N[0, 6] = 6).

(b) Let Ti be the arrival time of the ith costumer. Calculate Cov(T2, T4)

2.There are 8 students stepping into the elevator on the ground floor in the Hylan building (which has floors numbered {G, 1, 2, ..., 11}. Each one of the students needsto get to a floor which is chosen uniformly at random from {1, ..., 11}. Let Xi be a randomvariable that counts the number of students that stepped out on the ith floor. Find the covariance between X1 and X2