1. Random Variables and Stochastic Processes – 0903720 Lecture#13 Dr. Ghazi Al Sukkar Email: ghazi.alsukkar@ju.edu.joghazi.alsukkar@ju.edu.jo Office Hours: Refer to the website Course Website: http://www2.ju.edu.jo/sites/academic/ghazi.alsukkar 1

2. Chapter 6 Two Functions of Two Random Variables  Definition  Joint Density and the Jacobian  Examples for Continuous R.Vs  Auxiliary Variables  Example for Discrete R.Vs 2

3. Definition 3

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7. The marginals: 7

8. Joint Density 8

9. (a) (b) 9

10. (a) (b) 10

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20. And hence This gives And Notice that in this case the R.V.s U and V are not independent. 20

21. Auxiliary Variables 21

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28. Thus Represents the joint probability mass function of the random variables Z and W. 28

29. Also Thus Z represents a Geometric random variable since And 29

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