Find $\mathbb P(\frac{1}{4}<x<1)$ from the CDF given

Question

Cumulative distribution function of a random variable is given by

\begin{eqnarray} \mathbb F_X(x)= \left\{ \begin{array}{cc} 0 & x<0 \\ x^2 & 0\leq x<\frac{1}{2} \\ \frac{3}{4} & \frac{1}{2} \leq x<1 \\ 1 & x\geq 1 \end{array} \right. \end{eqnarray}

Find $\mathbb P(\frac{1}{4}<x<1)$?

Answer 1

Hint:

$\mathbb P(\frac{1}{4}<x<1)=F_X\left(1^{-}\right)-F_X(\frac{1}{4})$