Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The probability density function of the random variable $X$ is defined by $f(x) = \begin{cases} \frac{1}{18}(9 - x^2), & 0 \leq x \leq 3, \\ 0, & \text{otherwise}. \end{cases}$
(a)[3]

Find the value of $\mathrm{P}(X < 1.2)$.

(b)[3]

Find the value of $\mathrm{E}(X)$.

(c)[3]

Let $m$ be the median of $X$. Show that $m^3 - 27m + 27 = 0$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Uses $\dfrac{1}{18} \int_0^{1.2} (9 - x^2)\,dx$” …

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