See figure 411 find x y 0 1 figure 411 unit interval

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Unformatted text preview: ned for uo such that fX (uo ) > 0 by fY |X (v |uo ) = fX,Y (uo , v ) fX (uo ) − ∞ < v < +∞. (4.6) Graphically, the connection between fX,Y and fY |X (v |uo ) for uo fixed, is quite simple. For uo fixed, the right hand side of (4.6) depends on v in only one place; the denominator, fX (uo ), is just a constant. So fY |X (v |uo ) as a function of v is proportional to fX,Y (uo , v ), and the graph of fX,Y (uo , v ) with respect to v is obtained by slicing through the graph of the joint pdf along the line u ≡ uo in the u − v plane. The choice of the constant fX (uo ) in the denominator in (4.6) makes fY |X (v |uo ), as a function of v for uo fixed, itself a pdf. Indeed, it is nonnegative, and ∞ ∞ fY |X (v |uo )dv = −∞ −∞ fX,Y (uo , v ) 1 dv = fX (uo ) fX (uo ) ∞ fX,Y (uo , v )dv = −∞ fX (uo ) = 1. fX (uo ) In practice, given a value uo for X , we think of fY |X (v |uo ) as a new pdf for Y , based on our change of view due to observing the event X = uo . There is a bit of difficulty in this interp...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

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