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

[[math]] f_X(x) = \left \{ \begin{array}{ll} cx(1 - x), & \mbox{if $0 \lt x \lt 1$}, \\ 0, & \mbox{otherwise.} \end{array} \right. [[/math]]

• What is the value of [math]c[/math]?
• What is the cumulative distribution function [math]F_X[/math] for [math]X[/math]?
• What is the probability that [math]X \lt 1/4[/math]?