Q-1.An analyst develops the following probability distribution about the state of the economy and the market.

Which of the following statements about this probability distribution is least likely accurate?

A.The probability of a normal market is 0.30.

B.The probability of having a good economy and a bear market is 0.12.

C.Given that the economy is good, the chance of a poor economy and a bull market is 0.15.

D.Given that the economy is poor, the combined probability of a normal or a bull market is 0.50.

Solution: C

Given that the economy is good, the probability of a poor economy and a bull market is zero. The other statements are true. The P（normal market） = （0.60 × 0.30） + （0.40 × 0.30） = 0.30. P（good economy and bear market） = 0.60 × 0.20 = 0.12. Given that the economy is poor, the probability of a normal or bull market = 0.30 + 0.20 = 0.50.

Q-2.In country X, the probability that a letter sent through the postal system reaches its destination is 2/3. Assume that each postal delivery is independent of every other postal delivery, and assume that if a wife receives a letter from her husband, she will certainly mail a response to her husband. Suppose a man in country X mails a letter to his wife （also in country X） through the postal system. If the man does not receive a response letter from his wife, what is the probability that his wife received his letter?

A.1/3

B.3/5

C.2/3

D.2/5

Solution: D

（Notices: if the wife did not receive the letter, she would not send response to the man.）

Note:

A: the wife received the letter;

: the wife did not received the letter;

B: the man received a response letter from his wife;

:: the man did not receive a response letter from his wife

The question "If the man does not receive a response letter from his wife, what is the probability that his wife received his letter?" is equal to figure out P（A|Ë）。

Q-3.et X and Y be two random variables representing the annual returns of two different portfolios. If E[X] = 3, E[Y] = 4 and E[XY] = 11, then what is Cov[X, Y]?

A.-1

B.0

C.11

D.12

Solution: A

Q-4.An analyst gathered the following information about the return distributions for two portfolios during the same time period:

Portfolio Skewness Kurtosis

A -1.6 1.9

B 0.8 3.2

The analyst states that the distribution for Portfolio A is more peaked than a normal distribution and that the distribution for Portfolio B has a long tail on the left side of the distribution. Which of the following is correct?

A.The analyst's assessment is correct.

B.The analyst's assessment is correct for Portfolio A and incorrect for portfolio B.

C.The analyst's assessment is incorrect for Portfolio A but is correct for portfolio B.

D.The analyst is incorrect in his assessment for both portfolios.

Solution: D

The analyst's statement is incorrect in reference to either portfolio. Portfolio A has a kurtosis of less than 3, indicating that it is less peaked than a normal distribution （platykurtic）。 Portfolio B is positively skewed （long tail on the right side of the distribution）。

Q-5.Which type of distribution produces the lowest probability for a variable to exceed a specified extreme value X which is greater than the mean assuming the distributions all have the same mean and variance?

A.A leptokurtic distribution with a kurtosis of 4

B.A leptokurtic distribution with a kurtosis of 8

C.A normal distribution

D.A platykurtic distribution

Solution: D

A is incorrect. A leptokurtic distribution has fatter tails than the normal distribution. The kurtosis indicates the level of fatness in the tails, the higher the kurtosis, the fatter the tails. Therefore, the probability of exceeding a specified extreme value will be higher.

B is incorrect. Since answer A. has a lower kurtosis, a distribution with a kurtosis of 8 will necessarily produce a larger probability in the tails.

C is incorrect. By definition, a normal distribution has thinner tails than a leptokurtic distribution and larger tails than a platykurtic distribution.

D is correct. By definition, a platykurtic distribution has thinner tails than both the normal distribution and any leptokurtic distribution. Therefore, for an extreme value X, the lowest probability of exceeding it will be found in the distribution with the thinner tails.》》》點(diǎn)擊咨詢獲取CFA 一級(jí)免費(fèi)資料

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