| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Probability distribution from formula |
| Difficulty | Moderate -0.8 This is a straightforward probability distribution question requiring only direct substitution into given formulas and basic expectation/variance calculations. Part (i) is trivial arithmetic verification, parts (ii) and (iii) involve standard textbook procedures with no problem-solving insight needed. The formula is given, making this easier than average A-level statistics questions. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
Jeremy is a computing consultant who sometimes works at home. The number, $X$, of days that Jeremy works at home in any given week is modelled by the probability distribution
P($X = r$) = $\frac{1}{40}r(r + 1)$ for $r = 1, 2, 3, 4$.
\begin{enumerate}[label=(\roman*)]
\item Verify that P($X = 4$) = $\frac{1}{2}$. [1]
\item Calculate E($X$) and Var($X$). [5]
\item Jeremy works for 45 weeks each year. Find the expected number of weeks during which he works at home for exactly 2 days. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q3 [8]}}