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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 μ and standard deviation σ.
    (d) Calculate the mean and standard deviation of the sampling distribution of X obtained in part (b), and verify that these agree with μ and σ √2 , respectively.

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