Uncorrelated means that the covariance E[[XEx][YEy]] for X,Y is zero. Independence means that their densities can be factored into pieces which only depend on X and Y respectivly. Two variables X and Y are uncorrelated if E[[XEX][YEY]] = E[XY  XEY  YEX  EXEY] = E[XY]  EXEY = 0 i.e. EXY = EXEY The requirement for independence is much stronger it is Eg_1(X)g_2(Y) = Eg_1(X)Eg_2(Y) where g_1 and g_2 are arbitrary measurable (read functions which have a finite integrals) functions. hence, independence implies zero correlation but not the otherway around. Edited 10172002 12:35 PM
