{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ENMA 420-520 Lecture 5 Slides_1

# ENMA 420-520 Lecture 5 Slides_1 - Statistical Concepts for...

This preview shows pages 1–14. Sign up to view the full content.

Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #5 Bivariate Probability Distributions and Sampling Distributions 11

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

View Full Document
10/17/09 Joint Probability Distribution The joint probability distribution p(x,y) for two discrete random variables X and Y gives the values of p(x,y) for every combination of values of X and Y. Called a bivariate distribution Can be a table, graph or formula Requirements: 0 <= p(x,y) <= 1 for all values of X and Y 22
10/17/09 Marginal and Conditional Probability Distributions Given discrete random variables X and Y and their joint probability distribution p(x,y): The marginal (or unconditional) probability distributions of X and Y are: The conditional probability distributions are given by: 33

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

View Full Document
10/17/09 Exercise 6.2 44
10/17/09 Exercise 6.2 (Cont’d) 55

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

View Full Document
10/17/09 Exercise 6.6 Total Number of Combinations for 7 people & 3 positions: Then, need to determine the number of combinations of all three types for given X and Y. 66
10/17/09 Exercise 6.6 (Cont’d) 77 Notice the “not enough” p(0,0) and “too many” cases p(3,1), P(2,3), and P(3,2).

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

View Full Document
10/17/09 Exercise 6.6 (Cont’d) 88
10/17/09 5-minute Break Discuss examples of joint probability distributions. 99

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

View Full Document
10/17/09 Continuous Random Variables For continuous random variables X and Y: Bivariate joint probability density function: Marginal Density Functions: 1010
10/17/09 Exercise 6.10 1111

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

View Full Document
10/17/09 Exercise 6.12 1212
10/17/09 Expected Value of Two Random Variables Given g(x,y), a function of two random variables X and Y, the expected value of g(X,Y) is: 1313

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

View Full Document
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