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If Y1, . . . , Yn iid N(, 2 ), what is the sampling distribution of Y = n^(1) sigmai(=1 to n) Yi and

If Y1, . . . , Yn iid N(, 2 ), what is the sampling distribution of Y = n^(1) sigmai(=1 to n) Yi and S^2 = 1/(n1) * sigma (i=1 to n) (Yi Y )^2. Also, what is the mean and variance of Y and S^2?

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