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 0.115 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.)

Answer 1

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