Do The Math Q16

The stock prices of two companies at the end of any given year are modeled with random variables X and Y that follow a distribution with joint density function

What is the conditional variance of Y given that X = x ?

1. 1/12 Correct Answer
2. 7/6
3. x + 1/2
4. x² – 1/6
5. x² + x + 1/3

Solution: A

Let f1(x) denote the marginal density function of X. Then