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 that these two variables are independent, each with the pmf given in the accompanying table (so X₁, X₂ is a random sample of size n = 2).

x1	0	1	2
p(x1)	0.4	0.2	0.4

= 1, ² = 0.8(a)Determine the pmf of T_o = X₁ + X₂.

to	0	1	2	3	4
p(to)

(b)Calculate _To.

_To =

How does it relate to , the population mean?

_To =____

c)Calculate _To²._To² = How does it relate to ², the population variance?_To² = ²

(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 T_o = the sum of all four X_i's, what now are the values of E(T_o) and V(T_o)?E(T_o) =V(T_o) =

(e)Referring back to (d), what are the values of

P(T_o = 8) and P(T_o 7)

[Hint: Don't even think of listing all possible outcomes!]

P(T_o = 8)

=

P(T_o 7)

=