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What is the variance of a random sample of size 5 that is taken with replacement from a population with mean = 15 and  variance = 10?

Question

What is the variance of a random sample of size 5 that is taken with replacement from a population with mean = 15 and  variance = 10?

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Solution

The variance of a random sample taken with replacement from a population is equal to the population variance. This is because sampling with replacement means each sample is independent of the others. Therefore, the variance of a random sample of size 5 taken with replacement from a population with a variance of 10 is also 10.

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