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.
 Spring '08
 Zahrn
 The Land

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