# h8 - Statistics 5101 Fall 2010 Homework Assignment 8 Solve...

• Notes
• 3

This preview shows pages 1–2. Sign up to view the full content.

Statistics 5101, Fall 2010: Homework Assignment 8 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 8-1. Let X have the standard Cauchy distribution, which has PDF defined in the brand name distributions handout f ( x ) = 1 π · 1 1 + x 2 , -∞ < x < . (a) Find the quantile function for X . (b) Find the median of X . (c) Find the lower and upper quartiles of X . Hint: the indefinite integral of 1 / (1 + x 2 ) is arc tangent of x (inverse of the tangent function). 8-2. Suppose X has the Exp(1) distribution. (a) What is the best prediction of the value of X if minimizing expected squared error is the criterion? (b) What is the best prediction of the value of X if minimizing expected absolute error is the criterion? In this problem, we want numeric answers so we can see how different they are. 8-3. Suppose X has the Gam(2 , 1) distribution.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern