Graphing density probability functions

[RET80]

Homework Statement

let Y₁ and Y₂ have the joint probability density function given by:
8y₁y₂², 0 <= y₁ <= 1, 0 <= y₂ <= 1, y₁² <= y₂

0, otherwise

Homework Equations

Basic integrals? if they are even needed.

The Attempt at a Solution

I attempted it, by assuming 0 - 1 for y₁ and y₂ and got a square from 1 to 1 on y₁ to y₂

But assuming it's a square, it must be independent, and I continued the work and it is NOT independent, so the square shape would be wrong?

I'm not too sure on how to graph multi-variable functions like this in probability.

 

[Dick]

It's only the part of the square where (y1)^2<=y2. You didn't say what the problem is, but I think you just want to show the integral of 8*y1*y2^2 over that region is 1, right? Can you show us how you tried to do that?