Random Variables and Stochastic Processes – 0903720 Lecture#13 Dr. Ghazi Al Sukkar Office Hours:

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Random Variables and Stochastic Processes – Lecture#13 Dr. Ghazi Al Sukkar Office Hours: Refer to the website Course Website: 1

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

Definition 3

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The marginals: 7

Joint Density 8

(a) (b) 9

(a) (b) 10

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

Auxiliary Variables 21

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

Also Thus Z represents a Geometric random variable since And 29

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