6\\
\includegraphics[max width=\textwidth, alt={}, center]{1e20bcc7-a501-4df0-9d49-cca2db4c279a-3_371_504_260_534}\\
\includegraphics[max width=\textwidth, alt={}, center]{1e20bcc7-a501-4df0-9d49-cca2db4c279a-3_373_495_260_1123}\\
\includegraphics[max width=\textwidth, alt={}, center]{1e20bcc7-a501-4df0-9d49-cca2db4c279a-3_371_497_776_534}\\
\includegraphics[max width=\textwidth, alt={}, center]{1e20bcc7-a501-4df0-9d49-cca2db4c279a-3_367_488_778_1128}

The diagrams show the probability density functions of four random variables $W , X , Y$ and $Z$. Each of the four variables takes values between 0 and 3 only, and their medians are $m _ { W } , m _ { X } , m _ { Y }$ and $m _ { Z }$ respectively.\\
(i) List $m _ { W } , m _ { X } , m _ { Y }$ and $m _ { Z }$ in order of size, starting with the largest.\\
(ii) The probability density function of $X$ is given by

$$f ( x ) = \begin{cases} \frac { 4 } { 81 } x ^ { 3 } & 0 \leqslant x \leqslant 3 \\ 0 & \text { otherwise } \end{cases}$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\mathrm { E } ( X ) = \frac { 12 } { 5 }$.
\item Calculate $\mathrm { P } ( X > \mathrm { E } ( X ) )$.
\item Write down the value of $\mathrm { P } ( X < 2 \mathrm { E } ( X ) )$.
\end{enumerate}

\hfill \mbox{\textit{CAIE S2 2016 Q6 [9]}}