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% |

- 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% |

- 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

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) = 17**X, 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

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