Suppose a random variable Z is equal to the sum of two other random variables A and B which are related by the functional relationship B = A² – 2A – 4. Both A and B have a standard deviation of 3. Their correlation is 0.25. What is the standard deviation of Z?

This is a bit of a trick question. Its purpose is to emphasize to you the general applicability of formula [3.28]. To solve the problem, recognize that Z = A + B. You know the standard deviations and correlation of A and B, so you can directly apply [3.28] to obtain a standard deviation for Z. The result is 4.74. The information that B = A² – 2A – 4 is extraneous.