(a)[3]
Show that $k=\frac{3}{4}$ by using the fact that the total probability is $1$.
(b(i))[1]
State the value of $\mathrm{P}(X\leq m)$.
(b(ii))[5]
Hence, find $\mathrm{P}(\mathrm{E}(X)\leq X\leq m)$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
Let $X$ be a random variable with probability density function defined by $f(x)=\begin{cases}k(2x^2-x^3), & 0\leq x\leq 2,\\0, & \text{otherwise}.\end{cases}$ The median of $X$ is written as $m$.