Chapter 2.5 - Math3200 Intermediate Probability and Statistics Prof Nan Lin Department of Mathematics Washington University Outline Joint pdf(pmf

# Chapter 2.5 - Math3200 Intermediate Probability and...

• Notes
• 37

This preview shows page 1 - 9 out of 37 pages.

Math3200 Intermediate Probability and Statistics Prof. Nan Lin Department of Mathematics Washington University

Subscribe to view the full document.

Outline Joint pdf (pmf) Marginal distribution Independent random variables Conditional distribution Covariance Correlation coefficient Multivariate distribution
Joint distribution The joint distribution describes the simultaneous behavior of two (or more) random variables. For example: X : the length of one dimension of an injection-molded part, and Y : the length of another dimension. We might be interested in P(2.37 X 3.15 and 7.05 Y 7.88)

Subscribe to view the full document.

TWO DISCRETE RANDOM VARIABLES
Joint distribution Joint c.d.f. ? ?, ? = 𝑃 ? ≤ ?, ? ≤ ? = 𝑓(?, ?) ?≤? ?≤?

Subscribe to view the full document.

Marginal distribution
Example for joint probability mass function Consider the following table: Using the table, we have Y=0 Y=3 Y=4 X=5 1/7 1/7 1/7 3/7 X=8 3/7 0 1/7 4/7 4/7 1/7 2/7 p X p Y . 7 / 3 7 / 2 7 / 1 ) 4 ( p ) 3 ( p 3} P{Y 7 / 3 ) 5 ( p 7} P(X 2/7 p(5,4) p(5,3) 3} Y 7, P{X Y Y X

Subscribe to view the full document.

Expected Values for Jointly Distributed Random Variables Let X and Y be discrete random variables with joint probability mass function f(x, y). Let the sets of values of X and Y be A and B, respectively. We define E(X) and E(Y) as Example. For the random variables X and Y from the previous slide, ). , ( f E(Y) and ) , ( f ) ( f E(X) B XY A A XY B A X y x y y x x

### 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

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes