(a)[3]
Show that, indeed, $k = \dfrac{3}{a}$.
(b)[3]
Find the value of $a$ when $\text{E}(X) = 1$.
(c)[3]
Find the median value of $X$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The probability density function of the random variable $X$ is given by
$f(x) = \begin{cases} \dfrac{kx^2}{a^2}, & 0 \leq x \leq a, \\ 0, & \text{otherwise}, \end{cases}$
where $k$ and $a$ are positive constants.