joint distribution question

• April 6th 2008, 08:02 PM
lllll
joint distribution question
find the joint distribution of
$f(x,y) = \left\{ \begin{array}{rcl} 4xy & \mbox{for} & 0 \leq x \leq 1, 0 \leq y \leq 1 \\
0 \ \ \mbox{elsewhere}
\end{array}\right.$

considering the fact that it's continuous, you can't have a table with infinitively values, so do you just omit the table and approach it another way?
• April 6th 2008, 09:05 PM
mr fantastic
Quote:

Originally Posted by lllll
find the joint distribution of
$f(x,y) = \left\{ \begin{array}{rcl} 4xy & \mbox{for} & 0 \leq x \leq 1, 0 \leq y \leq 1 \\
0 \ \ \mbox{elsewhere}
\end{array}\right.$

considering the fact that it's continuous, you can't have a table with infinitively values, so do you just omit the table and approach it another way?

I'll give a detailed reply later when I have a chance (unless someone beats me to it)
• April 7th 2008, 12:23 AM
mr fantastic
Quote:

Originally Posted by lllll
find the joint distribution of
$f(x,y) = \left\{ \begin{array}{rcl} 4xy & \mbox{for} & 0 \leq x \leq 1, 0 \leq y \leq 1 \\
0 \ \ \mbox{elsewhere}
\end{array}\right.$

considering the fact that it's continuous, you can't have a table with infinitively values, so do you just omit the table and approach it another way?

I've had a closer look ...... are you trying to calculate $\Pr(X < x_1, Y < y_1)$. If so:

$\Pr(X < x_1, Y < y_1) = \int_{0}^{x_1} \int_{0}^{y_1} 4xy \, dy \, dx$.