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# lecture10 - ECE 5510 Random Processes Lecture Notes Fall...

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Unformatted text preview: ECE 5510: Random Processes Lecture Notes Fall 2009 Lecture 10 Today: (1) Conditional Joint pmfs and pdfs • Exam 1 Return: average = 88.1, Exam 1 stdev = 7.3. • HW 5 due Tuesday October 13 at 5pm in the HW locker. • Reading for today: Y&G 4.8-4.10, 5.4 • Reading for Tue, Oct 7: Y&G 4.7, 4.11, 5.6, 5.7 0.1 Review of Joint Distributions This is Sections 4.1-4.5. For two random variables X 1 and X 2 , • Joint CDF: F X 1 ,X 2 ( x 1 ,x 2 ) = P [ { X 1 ≤ x 1 } ∩ { X 2 ≤ x 2 } ] It is the probability that both events happen simultaneously. • Joint pmf: P X 1 ,X 2 ( x 1 ,x 2 ) = P [ { X 1 = x 1 } ∩ { X 2 = x 2 } ] It is the probability that both events happen simultaneously. • Joint pdf: f X 1 ,X 2 ( x 1 ,x 2 ) = ∂ 2 ∂x 1 ∂x 2 F X 1 ,X 2 ( x 1 ,x 2 ) The pmf and pdf still integrate/sum to one, and are non-negative. Now, to find a probability, you must double sum or double integrate. For example, for event B ∈ S , • Discrete case: P [ B ] = ∑∑ ( X 1 ,X 2 ) ∈ B P X 1 ,X 2 ( x 1 ,x 2 ) • Continuous Case: P [ B ] = integraltext integraltext ( X 1 ,X 2 ) ∈ B f X 1 ,X 2 ( x 1 ,x 2 ) We also talked about marginal distributions: • Marginal pmf: P X 2 ( x 2 ) = ∑ X 1 ∈ S X 1...
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lecture10 - ECE 5510 Random Processes Lecture Notes Fall...

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