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IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions

Which of the following statements about a simple random sample X1, ..., Xn from a population is correct?

The correct statement is that the observations are independent and identically distributed with the population distribution. This defines a random sample. Normality is not required, and the sample mean equals the population mean only on average, not in each sample.

  1. AThe Xi are independent and identically distributed with the population distributionCorrect
  2. BThe Xi must be normally distributed
  3. CThe sample mean always equals the population mean
  4. DSample values are dependent because they share the same population
  5. The sample variance is always larger than the population variance

Explanation

A random sample is defined as independent observations each with the population distribution. Normality is not required, and the sample mean only equals the population mean in expectation, not in every sample.

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