| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sum of Poisson processes |
| Type | Validity of Poisson model |
| Difficulty | Moderate -0.3 This is a straightforward S2 Poisson question requiring standard calculations: (i)(a) uses tables/calculator for P(X≥7) with λ=4.2, (i)(b) requires scaling λ to 0.42 for 1 year then calculating P(X=2), and (ii) tests understanding of Poisson assumptions. All techniques are routine for S2 with no problem-solving or novel insight required, making it slightly easier than average. |
| Spec | 5.02i Poisson distribution: random events model5.02k Calculate Poisson probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| "Cases of infection must occur randomly, independently, singly and at constant average rate" | B0 | |
| Above + "but it is contagious" | B1 | |
| Above + "but not independent as it is contagious" | B2 | |
| "Not independent as it is contagious" | B2 | |
| "Not constant average rate", or "not independent" | B0 | |
| "Not constant average rate because contagious" | B1 | *needs more* |
| "Not constant average rate because more likely at certain times of year" | B2 | |
| Probabilities change because of different susceptibilities | B0 | |
| Not constant average rate because of different susceptibilities | B2 | |
| Correct but with unjustified or wrong extra assertion | B1 | *scattergun* |
| More than one correct assertion, all justified | B2 | |
| Valid reason (e.g. "contagious") but not referred to conditions | B1 |
# Question 1 (Specimen Verbal):
| Answer | Mark | Guidance |
|--------|------|----------|
| "Cases of infection must occur randomly, independently, singly and at constant average rate" | B0 | |
| Above + "but it is contagious" | B1 | |
| Above + "but not independent as it is contagious" | B2 | |
| "Not independent as it is contagious" | B2 | |
| "Not constant average rate", or "not independent" | B0 | |
| "Not constant average rate because contagious" | B1 | *needs more* |
| "Not constant average rate because more likely at certain times of year" | B2 | |
| Probabilities change because of different susceptibilities | B0 | |
| Not constant average rate because of different susceptibilities | B2 | |
| Correct but with unjustified or wrong extra assertion | B1 | *scattergun* |
| More than one correct assertion, all justified | B2 | |
| Valid reason (e.g. "contagious") but not referred to conditions | B1 | |
---1 (i) The number of inhabitants of a village who are selected for jury service in the course of a 10-year period is a random variable with the distribution $\operatorname { Po } ( 4.2 )$.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that in the course of a 10-year period, at least 7 inhabitants are selected for jury service.
\item Find the probability that in 1 year, exactly 2 inhabitants are selected for jury service.\\
(ii) Explain why the number of inhabitants of the village who contract influenza in 1 year can probably not be well modelled by a Poisson distribution.
\end{enumerate}
\hfill \mbox{\textit{OCR S2 2010 Q1 [7]}}