GATE 2018 | MATHS | QUESTION 34

Question

Let the cumulative distribution function of the random variable \(X\) be given by
\[ F_X(x) = \begin{cases}
0 & \text{if } x < 0 \\
x & \text{if } 0 \leq x < \frac{1}{2} \\
\frac{1 + x}{2} & \text{if } \frac{1}{2} \leq x < 1 \\
1 & \text{if } x \geq 1
\end{cases}
\]

Then, the probability \(P(X = \frac{1}{2})\) is given by