This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 5.10 JOINT DISTRIBUTIONS/ DISCRETE and Continuous I. (P 173 175) Discrete Variables: (a) Joint distribution of X 1 and X 2 : f(x 1 ,x 2 ) = Pr(X 1 = x 1 , X 2 = x 2 ) (b)Marginal Distributions of X 1 and X 2 : f (x 1 ) = Pr ( X 1 =x 1 ) and f 2 (x 2 ) = Pr ( X 2 =x 2 ). Here f 1 (x 1 )= f(x 1 , x 2 ) (sum over all values of x 2 ). (c) Conditional probability distribution of X 1 given X 2 : f(x 1  x 2 ) = : f(x 1 ,x 2 )/ f 2 (x 2 ) for all x 1 ,x 2 provided f f 2 (x 2 ) 0. (d) Independent random variables : X 1 , and X 2 are independent if and only if f (x 1 ,x 2 ) = f 1 (x 1 ) f 2 (x 2 ). (e) Covariance of two random variable X 1 and X 2 = Cov(X 1 , X 2 ) = E(X 1 1 ) (X 2 2 ) . If X 1 and X 2 are independent then Cov(X 1 , X 2 ) =0. (f) Correlation between two random variables 12 = Cov(X 1 , X 2 ) / 1 2 where j denotes the standard deviation of X j for j=1,2. If X 1 , X 2 are independent then 12 = 0.0. Range for 12 is from 1 to +1. Here  12 =1.0 implies that X 2 = + X 1 and Var(X 2 X 1 ) =0.0, Note also that ( Cov(X 1 , X 2 ) = 12 1 2. ). Example: Two scanners are needed for an experiment . Of the five available 2 have electronic defects, another one has a defect in the memory and two are in good working order. Two units are selected at random. defect in the memory and two are in good working order....
View
Full
Document
This note was uploaded on 01/31/2008 for the course AMS 310.01 taught by Professor Mendell during the Fall '03 term at SUNY Stony Brook.
 Fall '03
 Mendell

Click to edit the document details