(a)[3]
Show that $\mathrm{E}(X)=\frac{11}{4}$.
(b)[3]
Find $\mathrm{Var}(X)$.
(c)[3]
If the median of $X$ is $m$, find $\mathrm{P}(m<X<3)$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
Let the random variable $X$ have probability density function given by $$f(x)=\begin{cases}\frac{3}{16}(4x-x^2), & 2 \leq x \leq 4, \\ 0, & \text{otherwise}.\end{cases}$$