I have density function $f(x,y)=4xy \mathbb{I}_{[0,1] \times [0,1]}(x,y)$.
I need to find: 1) $\mathbb{P}_F([0,1/3]\times[0,1/2])$
2) $\mathbb{P}_F([2/3,1]\times\mathbb{R})$
So in 1) I got $1/36$ I don’t know is it right, but I was integrating $f(x,y)$. Actually, I also find $\Delta_s F$ and got the same.
2) I can’t get the answer. Or the answer is 0. I am not sure. I was doing the same as in 1) Can somebody help me with this?
Answer to 2) is $\int_0^{1}\int_{2/3}^{1} 4xy dx dy=5/9$.