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Unformatted text preview: ]. The conditional density fX |Y (u|vo ) is undeﬁned if vo ≤ 0. For vo > 0 :
e−vo fX |Y (u|vo ) = = e−(u−vo ) u ≥ vo
else. That is, the conditional distribution of X given Y = vo is the exponential distribution with parameter one, shifted to the right by vo . The conditional pdfs are shown in Figure 4.10. Example 4.3.5 Suppose the unit interval [0, 1] is randomly divided into three subintervals by two
points, located as follows. The point X is uniformly distributed over the interval [0, 1]. Given
X = u, a second point is uniformly distributed over the interval [u, 1]. Let Y denote the length of
the middle subinterval. If the unit interval represents a stick, and the two points represent locations
of breaks, then X and Y are the lengths of the left and center sticks formed. See Figure 4.11. Find
X Y 0 1 Figure 4.11: Unit interval divided into intervals of length X , Y , and 1 − X − Y.
the pdf of Y.
Solution: We shall ﬁrst determine the joint pdf of X and Y ,...
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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 Institute of Technology.
- Spring '08
- The Land