| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Simple algebraic expression for P(X=x) |
| Difficulty | Standard +0.3 This is a straightforward probability distribution question requiring standard techniques: summing probabilities to find k, then calculating expectation and variance using definitions. The arithmetic is slightly tedious but the method is routine S1 content with no conceptual challenges or novel problem-solving required. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
The probability distribution of the random variable $X$ is given by the formula
$$\text{P}(X = r) = kr(r + 1) \quad \text{for } r = 1, 2, 3, 4, 5.$$
\begin{enumerate}[label=(\roman*)]
\item Show that $k = \frac{1}{70}$. [2]
\item Find E$(X)$ and Var$(X)$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2011 Q4 [7]}}