| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2001 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sum of Poisson processes |
| Type | Multi-period repeated application |
| Difficulty | Moderate -0.3 This is a straightforward application of the Poisson distribution with clearly stated rates. Part (a) is a simple verification calculation, part (b) requires scaling the rate parameter (λ = 0.9 × 6 = 5.4), and part (c) combines Poisson with binomial probability. All parts follow standard textbook procedures with no conceptual challenges or 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 |
2. On a stretch of motorway accidents occur at a rate of 0.9 per month.
\begin{enumerate}[label=(\alph*)]
\item Show that the probability of no accidents in the next month is 0.407 , to 3 significant figures.
Find the probability of
\item exactly 2 accidents in the next 6 month period,
\item no accidents in exactly 2 of the next 4 months.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2001 Q2 [7]}}