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

y
p(x,y)		0	1	2	total=P(X)
x	0	0.025	0.015	0.01	0.05
	1	0.05	0.03	0.02	0.1
	2	0.105	0.075	0.05	0.23
	3	0.15	0.09	0.06	0.3
	4	0.1	0.06	0.04	0.2
	5	0.05	0.03	0.04	0.12
total=P(Y)		0.48	0.3	0.22	1

X	P(X)	X*P(X)
0	0.050	0.000
1	0.100	0.100
2	0.230	0.460
3	0.300	0.900
4	0.200	0.800
5	0.120	0.600

mean = E[X] = Σx*P(X) =            2.86

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Y	P(Y)	Y*P(y)
0	0.480	0.000
1	0.300	0.300
2	0.220	0.440

mean = E[Y] = Σy*P(Y) =            0.74

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expected revenue from a single trip = $3*E(X) + $10*E(Y) = 3*2.86+10*0.74= $15.98(answer)