There are two traffic lights on a commuter’s route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 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).

x1 012 p(x1) .2 .5 .3

a. Determine the pmf of To X1 X2.

b. Calculate mTo

. How does it relate to m, the population mean?

c. Calculate To

. How does it relate to s2

, the population variance?

d. Let X3 and X4 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 To the sum of all four Xi

’s, what now are the values of E(To) and V(To)?

e. Referring back to (d), what are the values of P(To 8)

and P(To  7) [Hint: Don’t even think of listing all possible outcomes!]