[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

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

</math> f_X(x) = \left \{ \begin{array}{ll}

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

[[math]] \ltul\gt\ltli\gt What is the value of $c$? \lt/li\gt \ltli\gt What is the cumulative distribution function \ltmath\gtF_X[[/math]]

for [math]X[/math]?

What is the probability that [math]X \lt 1/4[/math]?