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13.4 Exercise 25

Avg difficulty 2.5

Use the central limit theorem to show that for large enough sample size (usually 20 or more), the sample average

A n = 1 n ∑ i = 1 n X i A_{n} = \frac{1}{n} \sum_{i = 1}^{n} X_{i}

is approximately N(μ,σ2/n)N \left(\mu , \sigma^{2} / n\right) for any reasonable population distribution having mean value μ and variance σ2.

Pfeiffer, Applied Probability, 13.4 Problems on Transform Methods, exercise 25

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.