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# Sampling Distribution of sample mean

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A population consists of the four numbers {0, 2, 4, 6}. Consider drawing a random sample of size 2 with replacement.

(a) List all possible samples and evaluate for each.
(b) Determine the sampling distribution of X.
(c) Write down the population distribution and calculate its mean &#956; and standard deviation &#963;.
(d) Calculate the mean and standard deviation of the sampling distribution of X obtained in part (b), and verify that these agree with &#956; and &#963; &#8730;2 , respectively.

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