Chapter 5: Problem 9
Let \(Y_{1}
Chapter 5: Problem 9
Let \(Y_{1}
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Get started for free. For \(\alpha>0\) and \(\beta>0\), consider the following accept/reject algorithm: (1) Generate \(U_{1}\) and \(U_{2}\) iid uniform \((0,1)\) random variables. Set \(V_{1}=U_{1}^{1 / \mathrm{a}}\) and \(V_{2}=U_{2}^{1 / \beta}\) (2) Set \(W=V_{1}+V_{2}\). If \(W \leq 1\), set \(X=V_{1} / W\), else go to Step (1). (3) Deliver \(X\).
Let \(Y_{1}
Let two independent random samples, each of size 10, from two normal distributions \(N\left(\mu_{1}, \sigma^{2}\right)\) and \(N\left(\mu_{2}, \sigma^{2}\right)\) yield \(\bar{x}=4.8, s_{1}^{2}=8.64, \bar{y}=5.6, s_{2}^{2}=7.88\). Find a 95 percent confidence interval for \(\mu_{1}-\mu_{2}\).
Let \(Y_{1}
Using the assumptions behind the confidence interval given in expression (5.4.17), show that $$ \sqrt{\frac{S_{1}^{2}}{n_{1}}+\frac{S_{2}^{2}}{n_{2}}} / \sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}} \stackrel{P}{\rightarrow} 1 $$
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