this is the question..:

yi ~ (µ,σ2) for I = 1,2,…,n. Then show that √n (ў - µ) ~ N (0,σ2)

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- Aug 9th 2008, 07:06 AM #1

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- Aug 9th 2008, 11:20 PM #4

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First the sum of independent normals is normal and hence so is the mean, also the expected value of sample mean is the population mean. Then the variance of a sum of independent RVs is equal to the sum of the variances so the variance of the sum of $\displaystyle n$ iid normals of variance $\displaystyle \sigma^2$ is $\displaystyle n \sigma^2 $.

RonL

- Aug 10th 2008, 01:03 AM #5