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Suppose we have a distribution of heights of all males in a country.

Let population size = N.

Now, I take a sample of 100 males = {h1,h2,h3,....h100}

How is the expected value of any data point, i.e., E(h1) = E(h2) = ..E(h100) = population mean?

NOTE: Every individual in the population equally likely to be included in the sample.

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  • $\begingroup$ Is every individual in the population equally likely to be included in the sample? $\endgroup$
    – Adrian
    Nov 25, 2021 at 1:36
  • $\begingroup$ Yes, every individual in the population equally likely to be included in the sample $\endgroup$ Nov 25, 2021 at 1:38

1 Answer 1

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Let $X_1,\cdots ,X_{100}\overset{iid}{\sim} F_X(x)$ for some distribution $F_X(x)$ that has an expected value $\mu$.

Since $X_1$ is distributed as $F_X(x)$, $\mathbb E[X_1]=\mu$. Since $X_2$ is distributed as $F_X(x)$,…

In the absence of other information about the subject, the value that you expect is the population value.

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