Thread: Finding Covariance of Continuous Probability Distributions

1. Finding Covariance of Continuous Probability Distributions

Can someone guide me through this problem or suggest how to start?

Let X and Y denote the value of two stocks at the end of a five-year period. X is uniformly distributed on the interval (0,12). Given X = x, Y is uniformly distributed on the interval (0, x). Determine Cov( X, Y ) according to this model.

2. Originally Posted by Walcott89
Can someone guide me through this problem or suggest how to start?

Let X and Y denote the value of two stocks at the end of a five-year period. X is uniformly distributed on the interval (0,12). Given X = x, Y is uniformly distributed on the interval (0, x). Determine Cov( X, Y ) according to this model.
The first step would be to get the joint pdf.

Spoiler:
Hey, at least try to get it before looking!
Spoiler:
*Ahem* ....
Spoiler:
$\displaystyle f(x, y) = \frac{1}{x} \cdot \frac{1}{12}$ for $\displaystyle 0 < y < x < 12$ and zero otherwise.