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What happens to the expected value of m as sample size increases?


As the sample size increases, the expected value of the sample mean (denoted as m) tends towards the population mean.

Suppose that we are given a population that has a fixed mean. We keep on drawing samples of larger and larger size in order to understand the population. We denote the sample mean as ‘m’.

Since the sample mean changes as we keep on drawing different samples, we can treat the sample mean as a random variable and calculate the expected value of the sample mean.

The weak law of large numbers tells us about the behaviour of the expected value of the sample mean. It tells us that the expected value of ‘m’ tends closer and closer to the population mean as the sample size increases.

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