| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 8 |
| Topic | Poisson distribution |
| Type | Expectation and variance of Poisson-related expressions |
| Difficulty | Moderate -0.8 This is a straightforward variance calculation question requiring only standard formulas. Part (a) involves finding x from probabilities summing to 1, then computing E(W) and E(W²) from a simple discrete distribution. Part (b) applies the basic variance transformation rule Var(aW+b)=a²Var(W). No conceptual insight or problem-solving required—purely mechanical application of A-level formulas. |
| Spec | 5.02b Expectation and variance: discrete random variables |
| \(w\) | 1 | 2 | 3 | 4 |
| \(\mathrm { P } ( W = w )\) | 0.25 | 0.36 | \(x\) | \(x ^ { 2 }\) |
1 The probability distribution for the discrete random variable $W$ is given in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$w$ & 1 & 2 & 3 & 4 \\
\hline
$\mathrm { P } ( W = w )$ & 0.25 & 0.36 & $x$ & $x ^ { 2 }$ \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Show that $\operatorname { Var } ( W ) = 0.8571$.
\item Find $\operatorname { Var } ( 3 W + 6 )$.
\end{enumerate}
\hfill \mbox{\textit{OCR FS1 AS 2021 Q1 [8]}}