(a)[3]
Show, by calculation, that $a = 2$.
(b)[4]
Find the median value of $X$.
(c)[3]
Find the exact value for $\text{E}(X)$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The random variable $X$ is described by the probability density function $f$, where
$f(x) = \begin{cases} ax - x^3, & 0 \leq x \leq \sqrt{2}, \\ 0, & \text{otherwise}, \end{cases}$
and $a$ is a constant.