Question

I need help with the following question from Mathematical Statistics.

Answer 1

This question requires knowledge of Calculus and Statistics.

Answer 2

The answer is A, but I keep getting -4wln(w) instead of -8wln(w).

Answer 3

Ok let me try it

Answer 4

Thank you!

Answer 5

\[\begin{align} F_W(w)&=P(W\le w)\\&=P(XY\le w)\\&= \iint\limits_{xy\le w} f_{X,Y}(x,y)\, dx\, dy\\&= \iint\limits_{\substack{
xy\le w \\
0\le x\le y\le1
}} 8xy \,dx \,dy \end{align}\]
Now to set up the iterated integral, I draw this diagram: