Question

Consider a small ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let X and Y denote the number of cars and buses, respectively, carried on a single trip. Suppose the joint distribution of X and Y is as given in the table below.

		y
p(x,y)		0	1	2
x	0	0.025	0.015	0.010
	1	0.050	0.030	0.020
	2	0.110	0.075	0.050
	3	0.150	0.090	0.060
	4	0.100	0.060	0.040
	5	0.050	0.030	0.035

Compute the expected revenue from a single trip. (Round your answer to two decimal places.)
$  

Answer 1

P(X = 0) = 0.025 + 0.015 + 0.01 = 0.05

P(X = 1) = 0.05 + 0.03 + 0.02 = 0.1

P(X = 2) = 0.11 + 0.075 + 0.05 = 0.235

P(X = 3) = 0.15 + 0.09 + 0.06 = 0.3

P(X = 4) = 0.1 + 0.06 + 0.04 = 0.2

P(X = 5) = 0.05 + 0.03 + 0.035 = 0.115

E(X) = 0 * 0.05 + 1 * 0.1 + 2 * 0.235 + 3 * 0.3 + 4 * 0.2 + 5 * 0.115 = 2.845

P(Y = 0) = 0.025 + 0.05 + 0.11 + 0.15 + 0.1 + 0.05 = 0.485

P(Y = 1) = 0.015 + 0.03 + 0.075 + 0.09 + 0.06 + 0.03 = 0.3

P(Y = 2) = 0.01 + 0.02 + 0.05 + 0.06 + 0.04 + 0.035 = 0.215

E(Y) = 0 * 0.485 + 1 * 0.3 + 2 * 0.215 = 0.73

Expected revenue = E(3X + 10Y) = 3 * E(X) + 10 * E(Y) = 3 * 2.845 + 10 * 0.73 = $15.84