I can't for the life of me figure this one out, I am stuck on part (c) ...
I have this as my starting point ?
$$ \frac{45}{304}\int_0^x\int_{2-x}^2 u^2v^2\,\mathrm{du} \mathrm{dv} $$
Here is my sketch for part a:
The problem I am having is that when I try to calculate the entire CDF for all ranges it sums to more than 1 :( which leads me to believe I am doing something wrong?
My CAS tells me
$$ \int\limits_0^x \int\limits_{2-x}^2 u^2 v^2 du dv = \frac{1}{3} \left( \frac{8}{3}- \frac{1}{3} (2-x)^3\right) x^3$$
This expressoin evaluated at $x=2$ is $\frac{64}{9}$ So $c$ should be chosen as $c=\frac{9}{64}$ and I think this is where the error was?