The correlation between any two random variables is always a value be-
tween +1 and –1.
Every random variable is perfectly correlated with itself, that is, the cor-
relation is 1.0.
Two random variables are said to be uncorrelated when the correlation
between them is 0.FORMULAS
Ifa,bare nonrandom numbers, then the following formulas hold:
E[aX+bY] = aE[X] + bE[Y]
var(aX+b) = a^2 var(X)
var(X+Y) = var(X) + var(Y) + 2cov(X,Y)
var(X–Y) = var(X) + var(Y) – 2cov(X,Y)
cov(aX,bY) = abcov(X,Y)
cov(X,Y+Z) = cov(X,Y) + cov(X,Z)
corr(aX,bY) = corr(X,Y)Introduction 13