MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Can you help me with this? I don’t know why but I keep getting the Variance for part A and B wrong
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. The joint probability mass function (pmf) of \( X \) and \( Y \) is given in the table below.

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

It is readily verified that \( X \) and \( Y \) are independent.

**(a) Compute the expected value, variance, and standard deviation of the total number of vehicles on a single trip.** (Round your standard deviation to two decimal places.)

- **Expected value:** 3.35 vehicles
- **Variance:** 11.75
- **Standard deviation:** 2.06 vehicles

**(b) If each car is charged $3 and each bus $10, compute the expected value (in $), variance, and standard deviation (in $) of the revenue resulting from a single trip.** (Round your standard deviation to two decimal places.)

- **Expected value:** $14.95
- **Variance:** [Incorrect value entered]
- **Standard deviation:** [Incorrect value entered]
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Transcribed Image Text: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. The joint probability mass function (pmf) of \( X \) and \( Y \) is given in the table below. | \( p(x, y) \) | \( y = 0 \) | \( y = 1 \) | \( y = 2 \) | |---------------|------------|------------|------------| | \( x = 0 \) | 0.100 | 0.060 | 0.040 | | \( x = 1 \) | 0.050 | 0.030 | 0.020 | | \( x = 2 \) | 0.125 | 0.075 | 0.050 | | \( x = 3 \) | 0.025 | 0.015 | 0.010 | | \( x = 4 \) | 0.025 | 0.015 | 0.010 | | \( x = 5 \) | 0.150 | 0.090 | 0.060 | It is readily verified that \( X \) and \( Y \) are independent. **(a) Compute the expected value, variance, and standard deviation of the total number of vehicles on a single trip.** (Round your standard deviation to two decimal places.) - **Expected value:** 3.35 vehicles - **Variance:** 11.75 - **Standard deviation:** 2.06 vehicles **(b) If each car is charged $3 and each bus $10, compute the expected value (in $), variance, and standard deviation (in $) of the revenue resulting from a single trip.** (Round your standard deviation to two decimal places.) - **Expected value:** $14.95 - **Variance:** [Incorrect value entered] - **Standard deviation:** [Incorrect value entered]
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