| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2016 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Sample mean distribution of Poisson |
| Difficulty | Standard +0.3 This is a straightforward application of standard Poisson distribution properties (sum of independent Poissons, sampling distribution of means) with routine calculations. Part (i) uses Po(3.9) for the sum, parts (ii)-(iii) apply CLT/normal approximation with given formulas. No novel insight required, just methodical application of learned techniques. |
| Spec | 5.02n Sum of Poisson variables: is Poisson5.04b Linear combinations: of normal distributions5.05a Sample mean distribution: central limit theorem |
$X$ and $Y$ are independent random variables with distributions $\mathrm{Po}(1.6)$ and $\mathrm{Po}(2.3)$ respectively.
\begin{enumerate}[label=(\roman*)]
\item Find $\mathrm{P}(X + Y = 4)$. [3]
\end{enumerate}
A random sample of 75 values of $X$ is taken.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item State the approximate distribution of the sample mean, $\overline{X}$, including the values of the parameters. [2]
\item Hence find the probability that the sample mean is more than 1.7. [3]
\item Explain whether the Central Limit theorem was needed to answer part (ii). [1]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2016 Q6 [9]}}