Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The probability density function graph $f$ for a random variable $X$ is symmetric about the line $x = 2$. It is stated that $\mathrm{P}(2 < X < 5) = \frac{117}{256}$.
(a)[2]
Using just this information, show that $\mathrm{P}(X > -1) = \frac{245}{256}$.
(b)[3]
It is now stated that, for $x$ in an appropriate domain, $f(x) = k(12 + 4x - x^2)$, where $k$ is a constant. Determine $k$.
(c)[5]
Another random variable $X$ has probability density function $g(x) = \frac{2}{9}(2 + x - x^2)$. The domain of $X$ consists of all $x$ values for which $g(x) \geq 0$. Determine $\mathrm{Var}(X)$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “By symmetry, for example $\frac12-\frac{117}{256}$” …