Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
A random variable $X$ has probability density function $f$. The plot of $f(x)$ is a horizontal line segment, parallel to the $x$-axis, running from $x = 0$ to $x = a$, where $a$ is a positive constant.
(a)[1]
State the median of $X$, in terms of $a$.
(b)[1]
Find $P\left(X > \frac{3}{4}a\right)$.
(c)[5]
Show that the variance of $X$ is $\frac{1}{12}a^2$.
(d)[2]
Given that $P(X < b) = p$, where $0 < b < \frac{1}{2}a$, find $P\left(\frac{1}{3}b < X < a - \frac{1}{3}b\right)$ in terms of $p$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtains $\text{E}(X)=\frac{a}{2}$” …