Ex:           If we have the following condition, what is the value of correlation, ?

Sol'n:      The covariance, σXY, appears in the numerator of the definition of correlation:

Substituting for the covariance yields the following:

The correlation is equal to one, meaning that X and Y are deterministically related.

This is in contrast to independent random variables that satisfy a similar form of equation for means:

Note that for independent random variables, the covariance is zero:

for X and Y independent