{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Hw01 - STAT 410 Homework#1(due Friday January 25 by 3:00...

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

STAT 410 Spring 2008 Homework #1 (due Friday, January 25, by 3:00 p.m.) 1. Consider a continuous random variable X with probability density function f X ( x ) = ° ± ° ² ³ < < o.w. 0 1 0 3 2 x x Find the moment-generating function of X, M X ( t ) . 2. Suppose a discrete random variable X has the following probability distribution: P( X = k ) = ( ) ! 2 ln k k , k = 1, 2, 3, … . a) Verify that this is a valid probability distribution. b) Find μ X = E ( X ) by finding the sum of the infinite series. c) Find the moment-generating function of X , M X ( t ) . d) Use M X ( t ) to find μ X = E ( X ) . 3. Suppose a random variable X has the following probability density function: ° ± ° ² ³ = - otherwise 0 1 0 ) ( x C x f x e a) What must the value of C be so that f ( x ) is a probability density function? b) Find the cumulative distribution function F ( x ) = P ( X x ) . c) Find the median of the probability distribution of X . d) Find μ X = E ( X ) .

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

View Full Document
4. Suppose a random variable X has the following probability density function: ° ± ° ² ³ = otherwise 0 1 1 ) ( C x x x f a) What must the value of
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