There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the com- muter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose these two variables are independent, each with pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). 0 1 2 x1 p(x) = 1.1, = .49 25 .3

a. Determine the pmf of T = X + X.

b. Calculate pr. How does it relate to , the population mean?

c. Calculate . How does it relate to , the population variance?

d. Let X and X be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With T = the sum of all four X's, what now are the values of E(T) and V(T)?

e. Referring back to (d), what are the values of P(T = 8) and P(T 7) [Hint: Don't even think of listing all pos- sible outcomes!]