> 
> We have $$F\_X(x) = \begin{cases} 0 & x \le 0 \\x & 0 < x \le 1 \\ 1 & x > 1 \end{cases}$$
> $$F\_T(x) = \begin{cases} 0 & x \le 0 \\ \dfrac{x}{2} & 0 < x \le 2 \\ 1 & x > 2 \end{cases}$$
> for two independent random variables $X$ and $Y$. Find the distribution of $Z = Y-X$.
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I have figured out that
$$F\_Z(z) = \int\_{-\infty}^{\infty} F\_Y(z+x)dF\_X(x)$$
but splitting the integral and calculating confuses me. The existence of $z$ makes it more difficult. Any help on calculating the integral is appreciated.