(a)[3]
Find the value of $P(X < 1.2)$.
(b)[3]
Find the value of $\text{E}(X)$.
(c)[3]
The median of $X$ is $m$. Show that $m^3 - 27m + 27 = 0$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
A random variable $X$ is defined by the probability density function given by $$f(x)=\begin{cases}\frac{1}{18}(9-x^2), & 0 \le x \le 3,\\ 0, & \text{otherwise}.\end{cases}$$