26、The manager of a pension fund determined that during the past five years 85% of the stocks in the portfolio have paid a dividend and 40% of the stocks have announced a stock split. If 95% of the stocks have paid a dividend and/or announced a stock split, the joint probability of a stock paying a dividend and announcing a stock split is closest to:

Select exactly 1 answer(s) from the following:

A. 10%.

B. 30%.

C. 45%.

D. 55%.

27、Which of the following statements about a normal distribution is least accurate? A normal distribution:

Select exactly 1 answer(s) from the following:

A. has a skewness of zero.

B. has an excess kurtosis of 3.

C. is completely described by two parameters.

D. can be the linear combination of two or more normal random variables.

28、A portfolio manager gathered the following information about four possible asset allocations:  

The manager's client has stated that her minimum acceptable return is 8%. Based on Roy's safety-first criterion, the most appropriate allocation is:

Select exactly 1 answer(s) from the following:

A. AllocationA.

B. AllocationB.

C. AllocationC.

D. AllocationD.

29、An analyst gathered the following information:

The standard error of the sample mean is closest to:

Select exactly 1 answer(s) from the following:

A. 0.47%.

B. 0.64%.

C. 0.80%.

D. 2.67%.

30、Compared to the normal distribution, the Student's t-distribution most likely:

Select exactly 1 answer(s) from the following:

A. has fatter tails.

B. is more peeked.

C. exhibits skewness.

D. has greater degrees of freedom.

答案和详解如下：

26 Correct answer is B

“Probability Concepts,” RichardA. Defusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkel
2008 Modular Level I, Vol. 1, pp. 325-326
Study Session 2-8-e
calculate and interpret 1) the joint probability of two events, 2) the probability that at least one of two events will occur, given the probability of each and the joint probability of the two events, and 3) a joint probability of any number of independent events
The probability that at least one of two events will occur is the sum of the probabilities of the separate events less the joint probability of the two events.
   P(A or
B) = P(A) + P(B) - P(AB)
   95% = 85% + 40% - P(AB); therefore P(AB) = 30%

27 Correct answer is B

“Common Probability Distributions,” RichardA. Defusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkel
2008 Modular Level I, Vol. 1, pp. 389-390
Study Session 2-9-f
explain the key properties of the normal distribution, distinguish between a univariate and a multivariate distribution, and explain the role of correlation in the multivariate normal distribution
A normal distribution has a kurtosis of 3. Its excess kurtosis (kurtosis - 3.0) equals zero.

28 Correct answer is B

“Common Probability Distributions,” RichardA. Defusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkel
2008 Modular Level I, Vol. 1, pp. 397-399
Study Session 2-9-i
define shortfall risk, calculate the safety-first ratio, andSelect an optimal portfolio using Roy’s safety-first criterion
Roy’s safety-first ratio = [E(RP) - RL] / σP
with the optimal portfolio having the highest ratio. The safety-first ratios for
the four allocations are:

29 Correct answer is C

“Sampling and Estimation,” RichardA. Defusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkel
2008 Modular Level I, Vol. 1, pp. 428-429
Study Session 2-10-e
calculate and interpret the standard error of the sample mean
The standard error of the sample mean is the sample standard deviation (or the population standard deviation if known) divided by the square root of the sample size. In this case, the standard error of the sample mean = 320.5 / 500.5 = 0.80%

30 Correct answer is A

“Sampling and Estimation,” RichardA. Defusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkel
2008 Modular Level I, Vol. 1, pp. 436-438
Study Session 2-10-i
describe the properties of Student’s t-distribution, and calculate and interpret its degrees of freedom
The Student’s t-distribution has fatter tails and is less peeked compared to the normal distribution.

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