Let $X,Y$ be independent random variables, uniform on $(0,1)$.
a) $P(X+Y>1.5)$.
b) $P(X>Y \mid X>1/2)$.
c) $P(\tan^{-1}(Y/X)
e) $E(\tan^{-1}(Y/X))$.
I could use the definitions I learned about joint distribution to solve part (a). But I am not sure how to approach the second one when there is conditional probability involves. And for the last two parts, I don't even know how to solve them when there is function like $\tan$ involves.