| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | State assumptions for geometric model |
| Difficulty | Moderate -0.8 This is a straightforward question testing basic knowledge of the geometric distribution. Part (i) requires recall of standard conditions, part (ii) involves direct application of formulas (single calculation for (a), simple complement rule for (b)), and part (iii) asks for a contextual observation about independence or constant probability. All parts are routine bookwork with minimal problem-solving, making this easier than average for A-level. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
Andy makes repeated attempts to thread a needle. The number of attempts up to and including his first success is denoted by $X$.
\begin{enumerate}[label=(\roman*)]
\item State two conditions necessary for $X$ to have a geometric distribution. [2]
\item Assuming that $X$ has the distribution Geo(0.3), find
\begin{enumerate}[label=(\alph*)]
\item P$(X = 5)$, [2]
\item P$(X > 5)$. [3]
\end{enumerate}
\item Suggest a reason why one of the conditions you have given in part (i) might not be satisfied in this context. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2010 Q1 [9]}}