(a)[3]
Show that, in this case, $k = \frac{a}{a - 1}$.
(b)[3]
Find $\text{E}(X)$ as a function of $a$.
(c)[4]
Find the 60th percentile of $X$ expressed in terms of $a$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
A random variable $X$ has probability density function defined by $$f(x) = \begin{cases} \frac{k}{x^2}, & 1 \le x \le a, \\ 0, & \text{otherwise}, \end{cases}$$ where $k$ and $a$ are positive constants.