(a)[3]
It is given that $\mathrm{E}(X) = \ln 2$. Prove that $b = 2a$.
(b)[3]
Show that $a = \frac{1}{2}$.
(c)[3]
Determine the median of $X$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The random variable $X$ is described by the probability density function $f$, where $$f(x) = \begin{cases} \frac{1}{x^2} & a < x < b, \\ 0 & \text{otherwise}, \end{cases}$$ and $a$ and $b$ are positive constants.