MULTIPLE RANDOM VARIABLES

This section briefly discusses some basic properties (without derivations) of multiple random variables. If X1 and X2 are two random variables and Y = X1+X2 then the following formulas are valid:

mean(Y) = mean(X1) + mean(X2)
var(Y)  = var(X1)  + var(X2) + 2*Covariance(X1,X2)

For the general case involving a sequence of random variables X1, X2, X3, ..., Xn, we have the following formulas:

Y = X1 + X2 + ... + Xn
          n
mean(Y) = SUM mean(Xi)
         i=0
          n
var(Y)  = SUM var (Xi) + SUM Covariance(Xi,Xj)
         i=0            i<j

If Xi and Xj are pairwise independent, then covariance(Xi,Xj) = 0, and therefore we have:

          n
var(Y)  = SUM var (Xi)
         i=0

Working With Two or More Variables

There are several constructs that you can use when you need to work with two or more variables, some of which are listed below:

• contingency table (useful for two categorical variables)

• contour plot

• hexagonal binning

...