Chapter 4 Joint Distribution Function of r V

Chapter 4 Joint Distribution & Function of r. V

Joint Discrete Distribution Definition

Joint discrete CDF

Example for joint distributions Consider the following table: Y=0 X=5 1/7 Y=3 1/7 Y=4 1/7 3/7 p. X X=8 3/7 0 4/7 1/7 p. Y Using the table, we have 4/7 2/7

The Marginal PDF

Example : Air Conditioner Maintenance – A company that services air conditioner units in residences and office blocks is interested in how to schedule its technicians in the most efficient manner – The random variable X, taking the values 1, 2, 3 and 4, is the service time in hours – The random variable Y, taking the values 1, 2 and 3, is the number of air conditioner units

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

• Joint p. d. f X=service time Y= number of units 1 2 3 4 1 0. 12 0. 08 0. 07 0. 05 2 0. 08 0. 15 0. 21 0. 13 3 0. 01 0. 02 0. 07 Find E[X] and E[Y] !! • Joint cdf