| Exam Board | OCR |
|---|---|
| Module | Further Statistics (Further Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Poisson distribution |
| Type | Two independent Poisson sums |
| Difficulty | Standard +0.3 This is a straightforward Further Statistics question testing standard Poisson distribution knowledge: stating conditions (textbook recall), writing the probability formula (direct recall), calculating a single probability (routine calculation), and finding a probability using sum of Poissons (standard technique with given bounds). All parts are routine applications with no problem-solving or novel insight required, making it slightly easier than average even for Further Maths. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02n Sum of Poisson variables: is Poisson |
The number of goals scored by the home team in a randomly chosen hockey match is denoted by $X$.
\begin{enumerate}[label=(\roman*)]
\item In order for $X$ to be modelled by a Poisson distribution it is assumed that goals scored are random events. State two other conditions needed for $X$ to be modelled by a Poisson distribution in this context. [2]
\end{enumerate}
Assume now that $X$ can be modelled by the distribution Po$(1.9)$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item \begin{enumerate}[label=(\alph*)]
\item Write down an expression for P$(X = r)$. [1]
\item Hence find P$(X = 3)$. [1]
\end{enumerate}
\item Assume also that the number of goals scored by the away team in a randomly chosen hockey match has an independent Poisson distribution with mean $\lambda$ between 1.31 and 1.32. Find an estimate for the probability that more than 3 goals are scored altogether in a randomly chosen match. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics 2017 Q5 [8]}}