Quantitative Methods MCQ - 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:

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:

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

53 The total cost of producing mugs is given by the equation: C = 2.5Q + 2000, where C is the total cost in dollars, USD2.5 is the variable cost per unit, Q is the number of units, and USD2000 is the fixed cost. The quantities and the probabilities of producing the respective quantities are given in the table below:

Probability	Quantity
0.30	200
0.50	300
0.20	400

The total expected cost of manufacturing mugs is closest to:

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?

The expected value of two independent random variables is the product of their own expected values.

55 The joint probabilities for X and Y are P(X=10, Y=5) = 0.3, and P(X=20, Y=8) = 0.7. The covariance of XY is closest to:

The joint probabilities in the question are given as follows:

X, Y	5	8
10	0.3
20		0.7

E(X) = 0.3 (10) + 0.7 (20) = 17
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