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I'm a little confused at this question posed by my prof. He asked us to generate a binomial distribution in R and input whatever variables we wanted.

x = rbinom(50, 10, 0.83)

Then he asks us to compute the sample mean, sample variance, population mean and population variance of the distribution.

sample mean:  mean(x)
sample var:   var(x)

But I have no idea what he intends we do to get the population mean and variance. Don't you need a larger set of data to be the population and a smaller set to be the sample? I only (seem to) have one set here.

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2 Answers 2

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The idea is that the population is so large that it can be adequately represented by the continuous binomial distribution. That is, whereas you compute the sample mean and sample variance from individual observations in the sample, the population is not treated as a huge sample of individuals, but as adequately described by a continuous distribution, whose mean and variance you can calculate analytically without sampling from it. If you were to take very large samples from the distribution, their mean and variance would tend to these analytically calculated values in the limit of infinite sample size.

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In your example, the population mean is $10\cdot0.83 = 8.3$ and the population variance is $10\cdot0.83\cdot(1-0.83)=1.411$.

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