Past exam of the mathematics course of the University of Cambridge / 2003 / ia / Paper 2 / 10F / i

The probabilities satisfy $a,b,c,d\ge 0$ and $a+b+c+d=1$. Since the variables are indicators,Their covariance isThus the necessary and sufficient condition for uncorrelated random variables isThis uses zero covariance as the definition. If one variable is constant, a normalized correlation coefficient is undefined, but zero covariance and this criterion remain meaningful.