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11ConditionalRVAnalysis

# 11ConditionalRVAnalysis - Conditional Distribution and...

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Click to edit Master subtitle style  EE 3180 Probability and  Conditional Distribution and  Density Functions Jeffrey B. Burl 11

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EE 3180 Probability and  The Conditional Distribution  Function n Conditional probability is defined: n Since the distribution function is a probability,  a conditional distribution function can be  define: 22 Pr( ) Pr( | ) , Pr( ) 0 Pr( ) A B A B B B B = Pr( ) ( | ) Pr( | ) , Pr( ) 0 Pr( ) x X x M F x M X x M M M B = =
EE 3180 Probability and  The Conditional Distribution  Function, Continued n The conditional distribution function is a  distribution function, i. e., has all the  properties of a distribution function: 33 0 ( | ) 1 for x F x M x - < < ( | ) 0 x F M - = ( | ) 1 x F M B = 2 1 2 1 ( | ) ( | ) if x x F x M F x M x x B

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EE 3180 Probability and  Using the Conditional  Distribution Function n Probabilities can be computed: 44 1 2 2 2 Pr( | ) ( | ) ( | ) x x x X x M F x M F x M < = - Pr( | ) ( | ) x X x M F x M B = Pr( | ) 1 ( | ) x X x M F x M = - 1 1 1 0 0 Pr( | ) ( | ) lim ( | ) x x X x M F x M F x M ε ε ε = = - - 1 2 2 1 0 0 Pr( | ) ( | ) lim ( | ) x x x X x M F x M F x M ε
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11ConditionalRVAnalysis - Conditional Distribution and...

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