Let y1, Y2, · ·· , Yn be a simple random sample of size n. Assume that sampling is with replacement. Recall that 1 y = - 1 Σ s2 = -> (Yi – - 9)°, Yi п — 1 i=1 i=1 µ: the population mean, o²: the...

Let y1, Y2, · ·· , Yn be a simple random sample of size n.<br>Assume that sampling is with<br>replacement. Recall that<br>1<br>y = -<br>1<br>Σ<br>s2 =<br>-> (Yi –<br>- 9)°,<br>Yi<br>п — 1<br>i=1<br>i=1<br>µ: the population mean, o²: the population variance, and T: population total.<br>(a) Show that E(s²) = o². That is, s? is unbiased estimator of o².<br>(b) Can you conclude that s is unbiased estimator of o? Explain.<br>(c) Derive unbiased estimator of o?, the variance of j.<br>(d) Derive unbiased estimator of o?, the variance of î.<br>

Extracted text: Let y1, Y2, · ·· , Yn be a simple random sample of size n. Assume that sampling is with replacement. Recall that 1 y = - 1 Σ s2 = -> (Yi – - 9)°, Yi п — 1 i=1 i=1 µ: the population mean, o²: the population variance, and T: population total. (a) Show that E(s²) = o². That is, s? is unbiased estimator of o². (b) Can you conclude that s is unbiased estimator of o? Explain. (c) Derive unbiased estimator of o?, the variance of j. (d) Derive unbiased estimator of o?, the variance of î.

Jun 10, 2022

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Let y1, Y2, · ·· , Yn be a simple random sample of size n. Assume that sampling is with replacement. Recall that 1 y = - 1 Σ s2 = -> (Yi – - 9)°, Yi п — 1 i=1 i=1 µ: the population mean, o²: the...

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