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

=========================

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

===================

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

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...

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
0.125
0.075
0.050
3
0.150
0.090
0.060
4
0.100
0.060...

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
0.085
0.075
0.050
3
0.150
0.090
0.060
4
0.100
0.060...

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
0.050
0.075
0.050
3
0.150
0.090
0.060
4
0.100
0.060...

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...

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y
p(x, y)
0
1
2
x
0
0.010
0.015
0.025
1
0.020
0.030
0.050
2
0.050
0.075
0.125
3
0.060
0.090
0.150
4
0.040
0.060
0.100
5
0.020
0.030
0.050
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0
1
2
x
0
0.010
0.015
0.025
1
0.020
0.030
0.050
2
0.050
0.075
0.125
3
0.060
0.090
0.150
4
0.040
0.060
0.100
5
0.020
0.030
0.050
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x
0
1
2
3
4
p(x)
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