BBy Bot
Jun 09'24
Exercise
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]?