Q1. Which of the following is an a priori probability?

A)   For a stock, based on prior patterns of up and down days, the probability of the stock having a down day tomorrow.

B)   On a random draw, the probability of choosing a stock of a particular industry from the S& 500.

C)   The probability the Fed will lower interest rates prior to the end of the year.

Q2. Each lottery ticket discloses the odds of winning. These odds are based on:

A)   a priori probability.

B)   past lottery history.

C)   the best estimate of the Department of Gaming.

Q3. Mital Tiene’s investment portfolio currently consists of stocks in two companies, 40% in Drysdahl Banking and the remaining amount in Clampett Oil. Performance measurement information for these two stocks is given in the table below:

Stock             Expected Return     Standard Deviation

Drysdahl Banking    10.50%          8.5%

Clampett Oil        16.55%           25.0%

The covariance between the two stocks is 0.001. Tiene is considering adding a third stock, Hilbilee Investors. Hilbilee Investor’s correlation coefficient with the current portfolio is 0.38.

Which of the following statements is least accurate?

A)   As Tiene diversifies, he will reduce the portfolio's unsystematic risk.

B)   The standard deviation of returns for the current portfolio is 15.5%.

C)   With Hilbilee added to the portfolio, the variance could be 0.026.

Q4. Last year, the average salary increase for poultry research assistants was 2.5%. Of the 10,000 poultry research

assistants, 2,000 received raises in excess of this amount. The odds that a randomly selected poultry research assistant received a salary increase in excess of 2.5% are:

A)   20%.

B)   1 to 4.

C)   1 to 5.

Q5. Which of the following statements about the defining properties of probability is most accurate?

A)   The probability of any event is between 0 and 1, exclusive.

B)   If the device that generates an event is not fair, the events can be mutually exclusive and exhaustive.

C)   The sum of the probabilities of events E₁ though E_x equals one if the events are mutually exclusive or exhaustive.

答案和详解如下：

Q1. Which of the following is an a priori probability?

A)   For a stock, based on prior patterns of up and down days, the probability of the stock having a down day tomorrow.

B)   On a random draw, the probability of choosing a stock of a particular industry from the S& 500.

C)   The probability the Fed will lower interest rates prior to the end of the year.

Correct answer is B)

A priori probability is based on formal reasoning and inspection. Given the number of stocks in the airline industry in the S&500 for example, the a priori probability of selecting an airline stock would be that number divided by 500.

Q2. Each lottery ticket discloses the odds of winning. These odds are based on:

A)   a priori probability.

B)   past lottery history.

C)   the best estimate of the Department of Gaming.

Correct answer is A)

An a priori probability is based on formal reasoning rather than on historical results or subjective opinion.

Q3. Mital Tiene’s investment portfolio currently consists of stocks in two companies, 40% in Drysdahl Banking and the remaining amount in Clampett Oil. Performance measurement information for these two stocks is given in the table below:

Stock             Expected Return     Standard Deviation

Drysdahl Banking    10.50%          8.5%

Clampett Oil        16.55%           25.0%

The covariance between the two stocks is 0.001. Tiene is considering adding a third stock, Hilbilee Investors. Hilbilee Investor’s correlation coefficient with the current portfolio is 0.38.

Which of the following statements is least accurate?

A)   As Tiene diversifies, he will reduce the portfolio's unsystematic risk.

B)   The standard deviation of returns for the current portfolio is 15.5%.

C)   With Hilbilee added to the portfolio, the variance could be 0.026.

Correct answer is C)

Since Hilbilee’s correlation coefficient with the existing portfolio is less than 1, there are benefits to diversification, and adding it to the existing portfolio would reduce the variance below the current level of 0.024. (See calculations below). The other choices are correct.

ER_Portfolio = (w_Drysdahl × ER_Drysdahl) + (w_Clampett × ER_Clampett) = (0.40 × 10.5%) + (0.60 × 16.55%) = 14.13%.

The equation for the standard deviation = σ_1,2 = [(w₁²)(σ₁²) + (w₂²)(σ₂²) + 2w₁w₂σ₁σ₂ρ_1,2]^1/2,

Here stock 1 = Drysdahl and stock 2 = Clampett, and r_1,2 = cov_1,2 / (σ₁ × σ₂) = 0.001 / (0.085 × 0.25) = 0.047

σ_Portfolio = [(0.40² × 0.085²) + (0.60² × 0.25²) + (2 × 0.40 × 0.60 × 0.085 × 0.25 × 0.047)]^1/2 = 0.024^1/2, or 0.155 = 15.5%. (The variance is 0.024).

Q4. Last year, the average salary increase for poultry research assistants was 2.5%. Of the 10,000 poultry research

assistants, 2,000 received raises in excess of this amount. The odds that a randomly selected poultry research assistant received a salary increase in excess of 2.5% are:

A)   20%.

B)   1 to 4.

C)   1 to 5.

Correct answer is B)         

For event “E,” the probability stated as odds is: P(E) / [1 – P(E)]. Here, the probability that a poultry research assistant received a salary increase in excess of 2.5% = 2,000 / 10,000 = 0.20, or 1/5 and the odds are (1/5) / [1 – (1/5)] = 1/4, or 1 to 4.

Q5. Which of the following statements about the defining properties of probability is most accurate?

A)   The probability of any event is between 0 and 1, exclusive.

B)   If the device that generates an event is not fair, the events can be mutually exclusive and exhaustive.

C)   The sum of the probabilities of events E₁ though E_x equals one if the events are mutually exclusive or exhaustive.

Correct answer is B)         

Even if the device that generates an event is not fair, the events can be mutually exclusive and exhaustive. Consider a standard die with the possible outcomes of 1,2,3,4,5 and 6. The P(2 or 4 or 6) = 0.50 and P(1 or 3 or 5) = 0.50, and thus the probabilities sum to 1 and are mutually exclusive and exhaustive. An unfair die would not change this.

Both remaining statements are false. The probability of any event is between 0 and 1, inclusive. It is possible that the probability of an event could equal 0 or 1, or any point in between. The sum of the probabilities of events E₁ though E_x equals 1 if the events are mutually exclusive and exhaustive.

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