| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | Mean/expectation of geometric distribution |
| Difficulty | Moderate -0.8 This is a straightforward application of standard geometric and binomial distribution formulas from S1. Part (i) requires direct substitution into geometric distribution probability formulas, part (ii) is recall of the expectation formula E(X)=1/p, and part (iii) is a standard binomial calculation. All parts are routine textbook exercises with no problem-solving or insight required. |
| Spec | 5.02c Linear coding: effects on mean and variance5.02f 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 |
3 Erika is a birdwatcher. The probability that she will see a woodpecker on any given day is $\frac { 1 } { 8 }$. It is assumed that this probability is unaffected by whether she has seen a woodpecker on any other day.\\
(i) Calculate the probability that Erika first sees a woodpecker
\begin{enumerate}[label=(\alph*)]
\item on the third day,
\item after the third day.\\
(ii) Find the expectation of the number of days up to and including the first day on which she sees a woodpecker.\\
(iii) Calculate the probability that she sees a woodpecker on exactly 2 days in the first 15 days.
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2009 Q3 [10]}}