Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!
<-- Previous | Newer --> | Current: 984142035 Dick Beldin at Fri, 09 Mar 2001 12:47:15 +0000.
back to [[Statistics/Assumptions]] When we assert that two or more [[Random Variables]] are independent, we imply that probabilities of compound events involving these variables can be calculated by simply multiplying the probabilities of the individual events. This is expressed in many ways. The most general statement is: *Pr[(X in A) & (Y in B)] = Pr[X in A]*Pr[Y in B] for A and B any subsets of the independent sample spaces for X and Y. In terms of joint and marginal probability densities, we find: *fXY(x,y)dx dy = fX(x)dx fY(y)dy where f represents a density and the indices on f indicate the random variable. In terms of the [[Expectation Operator]], we have: *E[X*Y] = E[X]*E[Y] ---- [[Dick Beldin]]