Solved: Suppose that Y1, Y2, . . . , Yn constitute a
Chapter 8, Problem 16E(choose chapter or problem)
Suppose that \(Y_{1}, Y_{2}, \ldots, \quad Y_{n}\) constitute a random sample from a normal distribution with parameters \(\mu \text { and } \sigma^{2}.
a. Show that \(S=\sqrt{S}^{2}\) is a biased estimator of \(\sigma\). [Hint: Recall the distribution of \((n-1) S^{2} / \sigma^{2}\) and the result given in Exercise 4.112.]
b. Adjust S to form an unbiased estimator of \(\sigma\)
c. Find an unbiased estimator of \(\mu-z_{\alpha} \sigma\), the point that cuts off a lower-tail area of \(\alpha\) under this normal curve.
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