Standard +0.3 This is a straightforward variance calculation requiring finding k from ΣP=1, computing E(Y) and E(Y²), then applying Var(aY+b)=a²Var(Y). All steps are routine applications of standard formulas with simple arithmetic (summing 2k(1+2+3+4)=1 gives k=1/20, then basic calculations). Slightly easier than average as it's purely mechanical with no problem-solving required.
6 The discrete random variable \(Y\) has the probability function
$$\mathrm { P } ( Y = y ) = \begin{cases} 2 k y & y = 1,2,3,4 \\ 0 & \text { otherwise } \end{cases}$$
where \(k\) is a constant.
Show that \(\operatorname { Var } ( 5 Y - 2 ) = 25\)
\includegraphics[max width=\textwidth, alt={}, center]{313cd5ce-07ff-4781-a134-565b8b221145-07_2488_1716_219_153}
6 The discrete random variable $Y$ has the probability function
$$\mathrm { P } ( Y = y ) = \begin{cases} 2 k y & y = 1,2,3,4 \\ 0 & \text { otherwise } \end{cases}$$
where $k$ is a constant.
Show that $\operatorname { Var } ( 5 Y - 2 ) = 25$\\
\includegraphics[max width=\textwidth, alt={}, center]{313cd5ce-07ff-4781-a134-565b8b221145-07_2488_1716_219_153}
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2018 Q6 [6]}}