Pg 59 - 27 Conditional Distributions Recall Section 1.7 Let...

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Unformatted text preview: 27 Conditional Distributions - Recall Section 1.7. Let A and B be any events in 8. Suppose A depends on B7 knowing B adds information about A. The conditional probability of A given B is denoted P(AjBi Pom B) P(A P(B‘) 3) a Let X and Y be continuous random variables with joint pdf fXJ-(Jr, y). The conditional distribution of X given Y : y is defined by fX,1"(:L-i y) f3" (y) for which the rules about mean and variance apply. it (IY :y) : o The conditional expected value of X given Y : y is “XI?” : E[XfY=yl : ] :zfxifi’:y)dr XEX o The conditional variance of X given 1’ :_ y is “in? : vai'lXiYZEl =/ (inflxiyffiii .rEX Y:y)d;t and can be found by vm-gxly : y] : E [my : MEE my : y] - Example: A soft drink machine has a random amount X in supply (meeeured in hundreds of gallons) at the beginning of a given day and dispenses a random amount Y during the day (measured in hundreds of gallons). Clearly, Y S X. X and Y have a joint distribution given by x/‘v flX,Y):%I<0snys2) (a) \Viiat IS the marginal distiibution of the amount of soft drink in supply? X 3%? stem/iii in Sopf’i/ )4 {he mom if'iefflnfl )fifx .41 59 oé ...
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