Answer¶
Cumulative Distribution of X can be found by integration and is as follows
\[
\begin{aligned}
f_{X}(x) = \begin{cases} 0 &\mbox{$x < 0$}\newline
0.5x &\mbox{$0 \leq x < 0.5$}\newline
0.75 &\mbox{x = 0.5}\newline
0.75 + 0.5(x-0.5) &\mbox{$0.5 < x \leq 1$} \newline
1 &\mbox {$1 < x$}\end{cases}
\end{aligned}
\]