(a)[1]
State the meaning of the constants $a$ and $b$ in this setting.
(b)[3]
Show that $a = \frac{b}{b+1}$.
(c)[4]
Given that $\text{E}(X)=\ln 3$, show that $b=2$ and determine the value of $a$.
(d)[3]
Find the median of $X$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The random variable $X$, measured in hours, for the time a very large group of people need to finish a challenge is described by the probability density function
$f(x)=\begin{cases}\frac{1}{x^2}, & a \le x \le b, \\ 0, & \text{otherwise},\end{cases}$
with $a$ and $b$ as constants.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly links the challenge context to the lower and upper completion times.” …
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