4 The table below shows the probability distribution for the number of students, $R$, attending classes for a particular mathematics module.

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
$\boldsymbol { r }$ & 6 & 7 & 8 \\
\hline
$\mathbf { P } ( \boldsymbol { R } = \boldsymbol { r } )$ & 0.1 & 0.6 & 0.3 \\
\hline
\end{tabular}
\end{center}

(a) Find values for $\mathrm { E } ( R )$ and $\operatorname { Var } ( R )$.\\
(b) The number of students, $S$, attending classes for a different mathematics module is such that

$$\mathrm { E } ( S ) = 10.9 , \quad \operatorname { Var } ( S ) = 1.69 \quad \text { and } \quad \rho _ { R S } = \frac { 2 } { 3 }$$

Find values for the mean and variance of:\\
(i) $T = R + S$;\\
(ii) $\quad D = S - R$.

\hfill \mbox{\textit{AQA S3  Q4}}