Quantitative Methods - Quantitative Methods Section 2
51. The probability distribution for a company’s dividend yield is as follows:
| Probability | Dividend Yield |
| 0.40 | 6.4% |
| 0.20 | 7.2% |
| 0.15 | 8.1% |
| 0.25 | 6.8% |
The expected value of the dividend yield is closest to:
- Option : B
- Explanation : The expected value of the dividend yield is the sum of the probabilityweighted average of the dividend yields. E(X) = (0.4 * 6.4) + (0.2 * 7.2) + (0.15 * 8.1) + (0.25 * 6.8) = 6.92%.
52. The probability distribution for the rate of return on a project is as follows:
| Probability | Rate of Return |
| 0.30 | 12.4% |
| 0.25 | 7.2% |
| 0.20 | 10.8% |
| 0.25 | 8.6% |
The variance for the above distribution is closest to:
- Option : B
- Explanation : α2 (X)= (0.30)(12.4−9.83)2+ (0.25)(7.2−9.83)2+ (0.20)(10.8−9.83)2+ (0.25)(8.60−9.83)2 = 4.28
| Probability | Quantity |
| 0.30 | 200 |
| 0.50 | 300 |
| 0.20 | 400 |
The total expected cost of manufacturing mugs is closest to:
- Option : A
- Explanation : First, calculate the expected number of units produced given the probabilities. E (Q) = (200 * 0.3) + (300 * 0.5) + (400 * 0.2) = 290 Use this in the equation to determine the total cost. Total cost = 2.5 (290) + 2000 = $2,725
54. Which of the following equations relating independent random variables is most likely correct?
- Option : A
- Explanation : The expected value of two independent random variables is the product of their own expected values.
- Option : C
- Explanation : The joint probabilities in the question are given as follows:
E(X) = 0.3 (10) + 0.7 (20) = 17X, Y 5 8 10 0.3 20 0.7
E(Y) = 0.3 (5) + 0.7 (8) = 7.1
Cov (XY) = 0.3 (10 - 17) (5 - 7.1) + 0.7 (20 - 17) (8 - 7.1) = 6.3
