The number of passengers including the driver in cars that c

The number of passengers (including the driver) in cars that cross a certain bridge is a random variable Y having mean E(Y) = 2.7 and variance V(Y) = 1.2. The toll on the bridge is $3.00 per car plus $0.50 per person in the car. The mean and variance of the total amount of money that is collected from a car that crosses the bridge are:

(a) mean = $8.60, variance = $.30

(b) mean = $4.35, variance = $3.30

(c) mean = $8.60, variance = $.60

(d) mean = $4.35, variance = $.30

(e) mean = $1.35, variance = $.30

Solution

The amount they pay in terms of Y is

A = 3.00 + 0.50Y

Thus,

E(A) = E(3.00 + 0.50Y) = 3.00 + 0.50E(Y) = 3.00 + 0.50*2.7

E(A) = 4.35

Also,

Var(A) = Var(3.00 + 0.50Y) = 0.50^2 Var(Y) = 0.50^2 * 1.2

Var(A) = 0.30

Thus, it is OPTION D. [ANSWER, D]