A random variable $$$X$$$ has probability density function given by $  f(x)= \begin{cases}\frac{1}{18}\left(9-x^{2}\right) &amp; 0 \leqslant x \leqslant 3 \\ 0 &amp; \text { otherwise. }\end{cases} $ The median of $$$X$$$ is $$$m$$$.  Show that $$$m^{3}-27 m+27=0$$$.  ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_63 Year：2021 Question No：4(c)

Answer:

$\frac{1}{18}\left[9 m-\frac{m^{3}}{3}\right]-0.5=0$
$m^{3}-27 m+27=0$

Knowledge points:

6.3.2 use a probability density function to solve problems involving probabilities, and to calculate the mean and variance of a distribution. (Including location of the median or other percentiles of a distribution by direct consideration of an area using the density function.) (Explicit knowledge of the cumulative distribution function is not included.)

Answer:

Knowledge points:

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