I have a question and I will be happy to get some help. $X$ and $Y$ are random variables that are distributed uniformly in $(0,1)$ (Continuous Uniform distribution). EDIT: X and Y are independent $W$ is defined as $X^2 - Y$. What is the probability density function of $W$? Similarly, $Z$ is defined as $X + Y$. What is the probability density function of $Z$?
I tried to calculate $\Pr(W<w)$ by using the definition of $W$ and calculating $\Pr(X^2 -Y < w)$ by calculating the double integral. Finally, to find the pdf, I differentiated the expression. I did the same for $Z$ but I am not sure about the results I have got (mainly how to determine the limits of the result). For example I have got for $W: f(w) = \sqrt{1+w} - \sqrt{w}$
thanks :)