CFA一級數(shù)量題目分享

第一道題目： Quantitative Methods

A bank offers a savings account with a stated annual rate of 3% in the first year and 5% in the second year. If returns are compounded quarterly and €90,000 is deposited in the account at the beginning of the first year, the account's value at the end of the second year is closest to:

A €97,200.

B €97,335.

C €97,455.

答案：

A. Incorrect because it fails to account for any compounding; (3% + 5%) = 8%; 90,000(1.08) = 97,200.

B. Incorrect because it fails to account for quarterly compounding; 90,000(1.03)(1.05) = 97,335.

C. Correct because the returns are compounded quarterly;

第二道題目： Quantitative Methods

Samples are drawn from a population that follows a binomial distribution with a probability of success on a trial of 0.3. According to the central limit theorem, as the sample size increases, the distribution of the sample mean approaches a:

A negatively skewed distribution.

B symmetric distribution.

C positively skewed distribution.

解析：

A. Incorrect because it is the underlying binomial distribution that exhibits skewness when p ≠ 0.5, not the sampling distribution of the sample mean. Since the sample size is large, the distribution of the sample mean will be approximately normal according to the central limit theorem, and therefore symmetric.

B. Correct because, according to the central limit theorem, the sampling distribution of the sample mean will be approximately normal when the sample size n is large. The normal distribution has a skewness of 0 (it is symmetric).  Since the binomial distribution has a mean of np and finite variance of np(1 – p), where n is the number of trials and p is the probability of success, the central limit theorem holds.

C. Incorrect because it is the underlying binomial distribution that exhibits skewness when p ≠ 0.5, not the sampling distribution of the sample mean. Since the sample size is large, the distribution of the sample mean will be approximately normal according to the central limit theorem, and therefore symmetric.