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FRM一级每日一题【风险管理基础33-定量分析】连续概率分布 II

来源：高顿网校 2015-03-04

　　习题：

　　Exercise:

　　Which of the following statements about sampling and the central limit theorem is least likely correct?

　　A The variance of the distribution of sample means is σ2/n.

　　B The central limit theorem may be used for large sample sizes for skewed distributions.

　　C The mean of the population and the mean of all possible sample means are always equal.

　　D The standard deviation of the mean of many observations is more than the standard deviation of a single observation.

　　解析：

　　Answer: D

　　Explanation: The central limit theorem holds for any distribution (skewed or not) as long as the sample size is large (i.e., n > 30). The mean of the population and the mean of the distribution of all sample means are equal. The standard deviation of the mean of many observations is less than the standard deviation of a single observation.

　　知识点：

　　Central Limit Theorem

　　The central limit theorem states that for simple random samples of size n from a population with a mean μ and a finite variance σ2, the sampling distribution of the sample mean approaches a normal probability distribution with mean μ and variance equal to as the sample size becomes large (usually means n ≥ 30).

　　Properties：

　　l If n ≥ 30, the sampling distribution of the sample means will be approximately normal.

　　l The mean of the population μ = the mean of the distribution of all possible sample means.

　　l The variance of the distribution of sample means is = the population variance divided by the sample size.
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