Let \(X\) and \(Y\) have joint density
\(f(x,y) = 90(y-x)^8, \quad 0<x<y<1\)
- State the marginal distribution for \(X\)
- State the marginal distribution for \(Y\)
- Are these two random variables independent?
- What is \(\mathbf{P}(Y > 2X)\)
- Fill in the blanks “The density \(f(x,y)\) above is the joint density of the _________ and __________ of ten independent uniform \((0,1)\) random variables.”
[Adapted from Pitman pg 354]