Science:Math Exam Resources/Courses/MATH105/April 2012/Question 04 (b)/Statement

Consider the function

$F(x)={\begin{cases}a&{\text{if }}x<0,\\k\arctan x&{\text{if }}0\leq x\leq 1,\\b&{\text{if }}x\geq 1.\end{cases}}$

(b) Let X be the continuous random variable with cummulative distribution function F(x) as given in part (a). Find the probability density function of X.