Let $X$ have a uniform distribution in unit interval $[0,1]$ and let $Y$ have an exponential distribution with parameter $=2$. Assume that $X$ and $Y$ are independent. Let $Z=X+Y$.
a) Find $P(YX)$.
b) Find the conditional PDF of $Z$ given $Y=y$.
c) Find the conditional PDF of $Y$ given that $Z=3$.
I am not sure how to express $P(YX)$ in general. Also, since it is stated that they are independent would this just amount to finding the $f_{XY}(x,y)$, which in this case would be equal to $f_X(x)\cdot{f}_Y(y)$? I know the function $f_{XY}(x,y)$ does not constitute a probability on its own, as it must be integrated over an interval but in this case what would that integral be?