Chapter 3: Problem 4
Let \(X\) be \(N\left(\mu, \sigma^{2}\right)\) so that \(P(X<89)=0.90\) and \(P(X<94)=0.95\). Find \(\mu\) and \(\sigma^{2}\).
Chapter 3: Problem 4
Let \(X\) be \(N\left(\mu, \sigma^{2}\right)\) so that \(P(X<89)=0.90\) and \(P(X<94)=0.95\). Find \(\mu\) and \(\sigma^{2}\).
All the tools & learning materials you need for study success - in one app.
Get started for freeShow that the graph of the \(\beta\) pdf is symmetric about the vertical line through \(x=\frac{1}{2}\) if \(\alpha=\beta\)
Let \(T=W / \sqrt{V / r}\), where the independent variables \(W\) and \(V\) are, respectively, normal with mean zero and variance 1 and chi-square with \(r\) degrees of freedom. Show that \(T^{2}\) has an \(F\) -distribution with parameters \(r_{1}=1\) and \(r_{2}=r\). Hint: What is the distribution of the numerator of \(T^{2} ?\)
If \(X\) is \(N(75,100)\), find \(P(X<60)\) and \(P(70
Let \(X\) have the uniform distribution with pdf \(f(x)=1,0
If \(X\) is \(N\left(\mu, \sigma^{2}\right)\), show that \(E(|X-\mu|)=\sigma \sqrt{2 / \pi}\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.