| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Multiple independent time periods |
| Difficulty | Moderate -0.3 This is a straightforward application of Poisson distribution requiring recall of conditions, basic probability calculations using tables/calculator, and understanding of independence across multiple trials. All parts are standard textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
The number of goals scored per match by Everly Rovers is represented by the random variable $X$ which has mean 1.8.
\begin{enumerate}[label=(\roman*)]
\item State two conditions for $X$ to be modelled by a Poisson distribution. [2]
\end{enumerate}
Assume now that $X \sim \text{Po}(1.8)$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find $\text{P}(2 < X < 6)$. [2]
\item The manager promises the team a bonus if they score at least 1 goal in each of the next 10 matches. Find the probability that they win the bonus. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2011 Q3 [7]}}