10 Example Class 8

10 Example Class 8 - THE UNIVERSITY OF HONG KONG DEPARTMENT...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 PROBABILITY AND STATISTICS I EXAMPLE CLASS 8 Review Conditional Distributions and Conditional Expectation For any two events E and F, the conditional probability of E given F is defined by P ( E | F ) = P ( E ∩ F ) P ( F ) provided that P(F) > Let ( X,Y ) be a discrete bivariate random vector with joint pmf p ( x,y ) and marginal pmfs p x ( x ) and p y ( y ). The conditional pmf of Y given that X = x is the function of y denoted by p Y | X ( y | x ), where p X ( x ) > p Y | X ( y | x ) = P ( Y = y | X = x ) = P ( Y = y,X = x ) P ( X = x ) = p ( x,y ) p X ( x ) If X is independent of Y, then the conditional pmf becomes p Y | X ( y | x ) = p ( x,y ) p X ( x ) = p X ( x ) p Y ( y ) p X ( x ) = p Y ( y ) For continuous random variables, the conditional distributions are defined as: f Y | X ( y | x ) = f ( x,y ) f X ( x ) provided that f X ( x ) > f X | Y ( x | y ) = f ( x,y ) f Y ( y ) provided that f Y (...
View Full Document

This note was uploaded on 05/04/2011 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

Page1 / 4

10 Example Class 8 - THE UNIVERSITY OF HONG KONG DEPARTMENT...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online