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Chapter 4

Chapter 4. Joint Distribution & Function of rV. Joint Discrete Distribution. Definition. Joint discrete CDF. Consider the following table: Using the table, we have. Example for joint distributions. Y=0 Y=3 Y=4.

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Chapter 4

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  1. Chapter 4 Joint Distribution & Function of rV

  2. Joint Discrete Distribution Definition

  3. Joint discrete CDF

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

  5. The Marginal PDF

  6. 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

  7. 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, Expected Values for Jointly Distributed Random Variables

  8. Joint p.d.f • Joint cdf Find E[X] and E[Y] !!

  9. Previously Example Marginal p.d.f of X Marginal p.d.f of Y

  10. Joint continuous distribution

  11. Th

  12. Ex a. Then find the joint CDF !

  13. The Marginal Continuous PDF Find From previously example

  14. Ex

  15. Independent rV

  16. Conditional pdf

  17. Joint MGF

  18. Group Discuss the exercise bellow ! BAIN, page : 166- No 7, 9, 21, 30 Time : 30’

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