1. MATHEMATICS IV: MA202
LECTURE 7

2. JOINT RANDOM VARIABLES|EXAMPLE
• The response time is the speed of page
downloads and it is critical for a mobile Web
site.
• As the response time increases, customers
become more frustrated and potentially
abandon the site for a competitive one.
• Let X denote the number of bars of service on
the mobile device.
• Let Y denote the response time (to the nearest
second) for a particular user and site.

3. JOINT PROBABILITY MASS FUNCTION
•

4. JOINT PROBABILITY DENSITY FUNCTION
•

5. EXAMPLE |SERVER ACCESS TIME
•
•

6. MARGINAL PROBABILITY DISTRIBUTION |
EXAMPLE
•

7. MARGINAL PROBABILITY DENSITY FUNCTION
•

8. MARGINAL PROBABILITY DENSITY FUNCTION|
EXAMPLE SERVER ACCESS TIME
•

9. CONDITIONAL PROBABILITY
DISTRIBUTION |EXAMPLE
•

10. CONDITIONAL PROBABILITY DENSITY
FUNCTION
• •

11. CONDITIONAL PROBABILITY| EXAMPLE
•
•

12. CONDITIONAL MEAN AND VARIANCE |
EXAMPLE
• •

13. INDEPENDENCE
•
•

14. INDEPENDENCE EXAMPLE
•
•

15. COVARIANCE
• •
When two or more random variables are defined on a
probability space, it is useful to describe how they vary
together.

16. COVARIANCE
•
•

17. COVARIANCE
Zero Covariance does not imply independence!

18. CORRELATION
There is another measure of the relationship
between two random variables that is usually
easier to interpret than covariance.
•