2020年CFA考试《CFA一级》考试共240题，分为单选题。小编为您整理Quantitative Methods5道练习题，附答案解析，供您备考练习。

1、The probability of event A is 40%. The probability of event B is 60%. The joint probability of AB is 40%. The probability that A or B occurs or both occur is closest to:【单选题】

A.40%.

B.60%.

C.84%.

正确答案:B

答案解析:“Probability Concepts,” Richard A. Defusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA
2011 Modular Level I, Vol. 1, pp. 443-445
Study Session 2-8-f
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.
P(A or B) = P(A) + P(B) – P(AB) = 40 + 60 - 40 = 60

2、A variable is normally distributed with a mean of 5.00 and a variance of 4.00. Calculate the probability of observing a value of negative 0.40 or less. That is, calculate P (Xi ≤ –0.40) given X is distributed as N(5, 4). Use this excerpt from the cumulative distribution function for the standard normal random variable table to calculate your answer.
Cumulative Probabilities for a Standard Normal Distribution
P(Z ≤ x) = N(x) for x ≥ 0 or P(Z ≤ z) = N(z) for z ≥ 0
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The calculated value is closest to:【单选题】

A.0.35%.

B.0.62%.

C.8.85%.

正确答案:A

答案解析:“Common Probability Distributions,” Richard A. DeFusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA
2013 Modular Level I, Vol. 1, Reading 9, Section 3.2
Study Session 3-9-c, l
Interpret a cumulative distribution function.
Determine the probability that a normally distributed random variable lies inside a given interval.
A is correct. First, standardize the value of interest, –0.40, for the given normal distribution:
Z = (X – μ)/σ = (–0.40 – 5.00)/2 = –2.70.
Then, use the given table of values to find the probability of a Z value being 2.70 standard deviations below the mean (i.e., when z ≤ 0). The value is 1 – P(Z ≤ +2.70).
In this problem, the solution is: 1 – 0.9965 = 0.0035 = 0.35%.

3、An analyst does research about Bollinger Bands.With respect to technical analysisindicators, Bollinger Bands depict a set number of standard deviations from:【单选题】

A.average return.

B.average price.

C.average volume.

正确答案:B

答案解析:布林线（Bollinger Bands）是由平均价格加上或减去几个标准差而画成的。

4、A stock is declining in price and reaches a price range wherein buying activity is sufficient to stop the decline. This is best described as a:【单选题】

A.support level.

B.resistance level.

C.change in polarity point.

正确答案:A

答案解析:“Technical Analysis,” Barry M. Sine, CFA and Robert A. Strong, CFA
2013 Modular Level I, Vol. 1, Reading 12, Section 3.2
Study Session 3– 12– c
Explain the uses of trend, support, resistance lines, and change in polarity.
A is correct Support level is defined to be “a low price range in which buying activity is sufficient to stop the decline in price.”

5、Based on historical returns, a portfolio has a Sharpe ratio of 2.0. If the mean return to the portfolio is20%, and the mean return to a risk-free asset is 4%, the standard deviation of return on the portfoliois closest to:【单选题】

A.12%.

B.8%.

C.10%.

正确答案:B

答案解析:The Sharpe ratio for a portfolio p, based on historical returns, is defined as
=(20%-4%)/2=8%.
CFA Level I
"Statistical Concepts and Market Returns," Richard A. DeFusco, Dennis W. McLeavey, Jerald E.Pinto, and David E. Runkle
Section 7.8