1. Tutorial 6, STAT1301 Fall 2010, 02NOV2010, MB103@HKU By Joseph Dong RANDOM V ECTOR

2. RECALL: CARTESIAN PRODUCT OF SETS Two discrete setsTwo Continuous sets 2

3. RECALL: SAMPLE SPACE OF A RANDOM VARIABLE 3

4. PrefixUni-Bi-Tri-Quadri-Quinti-Sexa-Septi-Octo-Novem-Deca- Num.12345678910 4

5. How to distribute total probability mass 1 on the sample space of the random vector? Is this process completely fixed? If not fixed, is this process completely arbitrary? If neither arbitrary, what are the rules for distributing total probability mass 1 onto this state space? “Marginal PDF/PMF” imposes an additive restriction. There is a lot to discover here… 5

6. INDEPENDENCE AMONG RANDOM VARIABLES 6

7. TWO RANDOM VARIABLES ARE INDEPENDENT IF… 7

8. INDEPENDENCE OF CONTINUOUS RANDOM VARIABLES 8

9. DETERMINE INDEPENDENCE SOLELY FROM THE JOINT DISTRIBUTION 9

10. 10

11. A SHORT SUMMARY FOR INDEPENDENT RANDOM VARIABLES 11

12. CONTINUOUS RANDOM VECTOR (OR JOINTLY CONTINUOUS RANDOM VARIABLES) 12

13. Check more properties of joint CDF and the relationship between joint CDF and joint PMF/PDF in the review part of handout. 13

14. EXERCISE TIME 14