2. There are two traf c lights on theway towork. Let X1 be the number of lights that are red, requiring a stop, and suppose that the distribution of X1 is as follows:

x1 0 1 2 p(x1) .2 .5 .3 m  1.1, s2  .49 Let X2 be the number of lights that are red on the way home; X2 is independent of X1. Assume that X2 has the same distribution as X1, so that X1, X2 is a random sample of size n  2.

a. Let To  X1  X2, and determine the probability distribution of To.

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

c. Calculate . How does it relate to s2, the population variance?