There are two traffic lights on my way to work. Let X1 be the number of lights at which I must stop, and suppose that the distribution of X1 is as follows:

x1 | 012
1.1, 2
.49 p(x1) | .2 .5 .3 Let X2 be the number of lights at which I must stop 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 To

. How does it relate to , the population mean?

c. Calculate 2 To

. How does it relate to 2

, the population variance?