However fxy u v is only equal to cu2 v 2 over a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ]. The conditional density fX |Y (u|vo ) is undefined if vo ≤ 0. For vo > 0 : e−u e−vo fX |Y (u|vo ) = = e−(u−vo ) u ≥ vo 0 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 ,...
View Full Document

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.

Ask a homework question - tutors are online