4. Consider the function F: R→ [0, 1] defined by
$$F(x) = \begin{cases}
0 & \text{if } x < 0 \\
x & \text{if } 0 \le x < \frac{1}{2} \\
\frac{1}{2} & \text{if } \frac{1}{2} \le x < 1 \\
x - \frac{1}{2} & \text{if } 1 \le x < \frac{3}{2} \\
1 & \text{if } x \ge \frac{3}{2}
\end{cases}$$
Show that F is a distribution function. Find pdf or pmf (if exists). Also compute
P(1 ≤ X < 3), where X has distribution function F.
[4 Marks]