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Consider an infinite population with 25% of the elements having the value 1, 25% the value 2, 25% the value 3, and 25% the value 4. If X is the value of a randomly selected item, then X is a discrete random variable whose possible values are 1, 2, 3, and 4.

(a) Find the population mean and population variance for the random variable X.

(b) List all 16 possible distinguishable samples of size 2, for each calculate the sample mean.

(c) Calculate the mean and variance of the distriubtion of X(bar) and show that, as expected, they are equal to the population mean and the (population variance)/n, respectively.

ok, (b) is fine, and I got the means to match from (a) and (c), but I can't figure out the variances.

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