(a)[3]
Show that $a = \dfrac{27}{2}$ is correct.
(b)[3]
Show that $\text{E}(X) = \dfrac{27}{2} \ln \dfrac{3}{2} - 3$ holds.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
A random variable $X$ is described by the probability density function $f$, where
$f(x) = \begin{cases} \dfrac{a}{x^2} - \dfrac{18}{x^3}, & 2 \leq x \leq 3, \\ 0, & \text{otherwise}, \end{cases}$
and $a$ is a constant.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Tries the integration $\int_2^3\left(a x^{-2}-18x^{-3}\right)dx$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI