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 0.115 0.075 0.050
3 0.150 0.090 0.060
4 0.100 0.060 0.040
Compute the expected revenue from a single trip. (Round your answer to two decimal places.)

Question

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Respuesta :

akiran007 akiran007 · Answer 1 · 2021-01-07T14:40:18+01:00

Answer:

Expected revenue from the single trip is $ 13.14

Step-by-step explanation:

y

p(x,y) 0 1 2 g(x)

x 0 0.025 0.015 0.010 0.05

1 0.050 0.030 0.020 0.1

2 0.115 0.075 0.050 0.24

3 0.150 0.090 0.060 0.3

4 0.100 0.060 0.040 0.2

h(y) 0.325 0.27 0.18

E (x+Y) = E(X) +E(Y)

E(X)= ∑ xi g(x)i

= ( 0*0.05) + (1*0.1) + (2* 0.24) + (3*0.3) + (4*0.2)

= 0 + 0.1+ 0.48 + 0.9+0.8

=2.28

E(Y)= ∑yi h(y)

= (0* 0.325) + (1*0.27) + (2*0.18)

= 0 +0.27+ 0.36

= 0.63

E (x+Y) = E(X) +E(Y)

= 2.28 + 0.63

= 2.91

But the equation is 3x+ 10y

E(3x+ 10y)= 3E(x) + 10 E(y)

= 3(2.28) + 10 (0.63)

= 6.84 +6.3

= 13.14

Expected revenue from the single trip is $ 13.14