| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Discrete Probability Distributions |
| Type | Two unknowns from sum and expectation |
| Difficulty | Standard +0.3 This is a standard Further Statistics question requiring systematic application of probability axioms and variance properties. Students must use ΣP=1 and E(W)=1.61 to form two equations in x and y, solve simultaneously, calculate E(W²), find Var(W), then apply the linear transformation rule Var(aW+b)=a²Var(W). While multi-step, each technique is routine for FS1 and follows a predictable structure, making it slightly easier than average A-level difficulty. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| \(w\) | 0 | 1 | 2 | 3 |
| \(\mathrm{P}(W = w)\) | 0.19 | 0.18 | \(x\) | \(y\) |
The probability distribution of a discrete random variable $W$ is given in the table.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
$w$ & 0 & 1 & 2 & 3 \\
\hline
$\mathrm{P}(W = w)$ & 0.19 & 0.18 & $x$ & $y$ \\
\hline
\end{tabular}
\end{center}
Given that $\mathrm{E}(W) = 1.61$, find the value of $\text{Var}(3W + 2)$. [7]
\hfill \mbox{\textit{OCR FS1 AS 2017 Q2 [7]}}