(a)[2]
Express $b$ in terms of $a$.
(b)[5]
With $\text{E}(X)=\frac{4}{9}$ given, determine the value of $a$.
(c)[4]
With the value of $a$ from part (b), determine $k$ such that $\mathrm{P}(X<k)=\frac{3}{4}$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The graph of the probability density function, $f$, for the random variable $X$ is shown. It is a straight line joining $(0, a)$ to $(b, 0)$, with $a$ and $b$ as constants. Outside this interval, $f(x)=0$.