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	0.105	0.075	0.050
	3	0.150	0.090	0.060
	4	0.100	0.060	0.040
	5	0.050	0.030	0.040

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

Answer 1

X	P(X)	X.P(X)
0	0.025+0.015+0.010 = 0.05	0.00
1	0.050+0.030+0.020 = 0.10	0.10
2	0.105+0.075+0.050 = 0.23	0.46
3	0.150+0.090+0.060 = 0.30	0.90
4	0.100+0.060+0.040 = 0.20	0.80
5	0.050+0.030+0.040 = 0.12	0.60
Total	1.00	2.86

E(x) = Ʃ x*p(x) = 2.86

Y	P(Y)	Y.P(Y)
0	0.025+0.050+0.105+0.150+0.100+0.050 = 0.48	0.00
1	0.015+0.030+0.075+0.090+0.060+0.030 = 0.30	0.30
2	0.010+0.020+0.050+0.060+0.040+0.040 = 0.22	0.44
Total	1.00	0.74

E(y) = Ʃ y*p(y) = 0.74

Expected revenue for a single trip = $3* 2.86 + $10*0.74 = $15.98