# HW2 - STAT 410 Homework#2(due Friday September 12 by 3:00...

This preview shows pages 1–3. Sign up to view the full content.

STAT 410 Fall 2008 Homework #2 (due Friday, September 12, by 3:00 p.m.) 1. ( ~ 1.9.19 ) Let X be a nonnegative continuous random variable with p.d.f. f ( x ) and c.d.f. F ( x ) . Show that E ( X ) = ( ) ( ) ° - 0 1 x x d F . 2. Suppose that X follows a uniform distribution on the interval [ π / 2 , π / 2 ] . Find the c.d.f. and the p.d.f. of Y = tan X. 3. An insurance policy reimburses a loss up to a benefit limit of 10. The policyholder’s loss, Y , follows a distribution with density function: f ( y ) = ± ± ² ± ± ³ ´ > otherwise 0 1 if 2 3 y y What is the expected value and the variance of the benefit paid under the insurance policy?

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

View Full Document
4. The time, T , that a manufacturing system is out of operation has cumulative distribution function F ( t ) = ± ± ² ± ± ³ ´ > µ · ¸ ¹ º - otherwise 0 2 if 2 1 2 t t The resulting cost to the company is Y = T 2 . Determine the density function of Y . 5. Suppose that X is distributed with density given by f ( x ) = ± ± ² ± ± ³ ´ > otherwise 0 1 if 2 3 x x a) Calculate the mean of X.
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