(a)[3]
Show that $k=\frac{1}{\pi}$.
(b)[3]
Confirm that the median of $X$ is between $0.83$ and $0.84$.
(c)[4]
Find the exact value of $\mathrm{E}(X)$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The probability density function, $f$, for the random variable $X$ is defined by
$f(x)=\begin{cases}k(1+\cos x), & 0 \le x \le \pi,\\ 0, & \text{otherwise},\end{cases}$
where $k$ denotes a constant.