| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2011 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sum of Poisson processes |
| Type | Joint probability of independent events |
| Difficulty | Standard +0.3 This is a straightforward application of Poisson distribution formulas with standard calculations. Part (a) requires basic Poisson probability calculations and independence assumption; part (b) tests understanding of independence; part (c) involves scaling Poisson parameters and using normal approximation. All techniques are routine for S2 level with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities5.02n Sum of Poisson variables: is Poisson |
3 Lucy is the captain of her school's cricket team.\\
The number of catches, $X$, taken by Lucy during any particular cricket match may be modelled by a Poisson distribution with mean 0.6 .
The number of run-outs, $Y$, effected by Lucy during any particular cricket match may be modelled by a Poisson distribution with mean 0.15 .
\begin{enumerate}[label=(\alph*)]
\item Find:
\begin{enumerate}[label=(\roman*)]
\item $\mathrm { P } ( X \leqslant 1 )$;
\item $\mathrm { P } ( X \leqslant 1$ and $Y \geqslant 1 )$.
\end{enumerate}\item State the assumption that you made in answering part (a)(ii).
\item During a particular season, Lucy plays in 16 cricket matches.
\begin{enumerate}[label=(\roman*)]
\item Calculate the probability that the number of catches taken by Lucy during this season is exactly 10 .
\item Determine the probability that the total number of catches taken and run-outs effected by Lucy during this season is at least 15 .
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S2 2011 Q3 [11]}}