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lecture15 - Stat 302 Introduction to Probability Jiahua...

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Stat 302, Introduction to Probability Jiahua Chen January-April 2011 Jiahua Chen () Lecture 15 January-April 2011 1 / 14

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Conditional Distribution; discrete case Let X and Y be two discrete random variables with joint pmf given by p ( x ; y ) . In other words, P ( X = x , Y = y ) = p ( x , y ) . We may directly deFne two events A = { ω : X ( ω ) = x } ; B = { ω : Y ( ω ) = y } and state that p ( x , y ) = P ( A B ) = P ( AB ) . Jiahua Chen () Lecture 15 January-April 2011 2 / 14
Conditional Distribution; discrete case Keeping the defnition A = { ω : X ( ω ) = x } ; B = { ω : Y ( ω ) = y } we may be interested in computing P ( B | A ) = P ( AB ) P ( A ) = p ( x , y ) p X ( x ) . For instance, X and Y could be the number o± hits at a popular website on two consecutive days. Knowing X = 1432, what would be Y , the number o± hits tomorrow? Jiahua Chen () Lecture 15 January-April 2011 3 / 14

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Conditional Distribution; discrete case The answer is related to computing P ( Y = y | X = 1432 ) . In general, we call
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