Let [math]X[/math] be a random variable with cumulative distribution function

[[math]] F(x) = \left \{ \begin{array}{ll} 0, & \mbox{if $x \lt 0$}, \\ \sin^2(\pi x/2), & \mbox{if $0 \leq x \leq 1$}, \\ 1, & \mbox{if $1 \lt x $}. \end{array} \right. [[/math]]

• What is the density function [math]f_X[/math] for [math]X[/math]?
• What is the probability that [math]X \lt 1/4[/math]?