| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Sequential trials until success |
| Difficulty | Moderate -0.8 This is a straightforward geometric distribution problem with a given probability table. Part (i) requires routine calculation of E(X) and Var(X) using standard formulas, part (ii) is a simple linear transformation, and part (iii) asks for a basic diagram. All calculations are direct applications of memorized formulas with no problem-solving or insight required. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(r\) | 1 | 2 | 3 | 4 |
| \(\mathrm { P } ( X = r )\) | 0.2 | 0.16 | 0.128 | 0.512 |
7 A company is searching for oil reserves. The company has purchased the rights to make test drillings at four sites. It investigates these sites one at a time but, if oil is found, it does not proceed to any further sites. At each site, there is probability 0.2 of finding oil, independently of all other sites.
The random variable $X$ represents the number of sites investigated. The probability distribution of $X$ is shown below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$r$ & 1 & 2 & 3 & 4 \\
\hline
$\mathrm { P } ( X = r )$ & 0.2 & 0.16 & 0.128 & 0.512 \\
\hline
\end{tabular}
\end{center}
(i) Find the expectation and variance of $X$.\\
(ii) It costs $\pounds 45000$ to investigate each site. Find the expected total cost of the investigation.\\
(iii) Draw a suitable diagram to illustrate the distribution of $X$.
\hfill \mbox{\textit{OCR MEI S1 Q7 [8]}}