There are two traffic lights on a commuter’s route to and from work. Let X1 be the numbe...

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).

a. Determine the pmf of To = X₁ + X₂.

b. Calculate σ²_To. How does it relate to μ, the population mean?

c. Calculate T_o. How does it relate to σ², 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 T_o = the sum of all four X_i’s, what now are the values of E(T_o) and 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!]