1. Statistics 270 - Lecture 18

2. Will begin Chapter 5 today

3. Many situations where one is interested in more than one random variable Have a joint distribution for such cases

4. Example Let X and Y be random variables with pmf

5. Definition Let X and Y be rv’s on a sample space S Discrete rv’s: The joint prob. mass function for each (x,y) is defined by p(x,y)=P(X=x, Y=y) If A is an event then,

6. Discrete RV’s Usual properties of pmf’s still hold

7. Example Let X and Y be random variables with pmf Observations: P(X=2,Y=2)= P(X>1, Y=1)

8. Example Let X be the number of Canon digital cameras sold in a week at a certain store The pmf for X is 60% of all customers who purchase camera also purchase the long- term warranty Determine the joint pdf of X and Y

9. Definition The marginal probability mass function for discrete random varaibles X and Y, denote by p X (x) and p Y (y), respectively, are given by

10. Example Let X be the number of Canon digital cameras sold in a week at a certain store The pmf for X is 60% of all customers who purchase camera also purchase the long- term warranty Find the marginal distributions of X and Y

11. Definition Let X and Y be rv’s on a sample space S Continuous rv’s: The joint prob. Distribution function for (x,y) is defined by f(x,y) If A is an event then,

12. Continuous rv’s Usual properties of pdf’s still hold

13. Example: The front tire on a particular type of car is suppose to be filled to a pressure of 26 psi Suppose the actual air pressure in EACH tire is a random variable (X for the right side; Y for the left side) with joint pdf Notice that they seem to vary jointly