| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Calculate Var(X) from table |
| Difficulty | Moderate -0.8 This is a straightforward S1 probability distribution question requiring basic combinatorics (selecting 2 from 5 notes) and standard expectation/variance calculations using given formulas. The probability calculations are simple enumeration, and E(X) and Var(X) follow directly from textbook methods with no conceptual challenges—easier than average A-level. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(r\) | 10 | 15 | 20 | 25 | 30 |
| P(X = r) | 0.1 | 0.4 | 0.1 | 0.2 | 0.2 |
In her purse, Katharine has two £5 notes, two £10 notes and one £20 note. She decides to select two of these notes at random to donate to a charity. The total value of these two notes is denoted by the random variable $£X$.
\begin{enumerate}[label=(\roman*)]
\item \begin{enumerate}[label=(\alph*)]
\item Show that P(X = 10) = 0.1. [1]
\item Show that P(X = 30) = 0.2. [2]
\end{enumerate}
The table shows the probability distribution of X.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$r$ & 10 & 15 & 20 & 25 & 30 \\
\hline
P(X = r) & 0.1 & 0.4 & 0.1 & 0.2 & 0.2 \\
\hline
\end{tabular}
\end{center}
\item Find E(X) and Var(X). [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2010 Q2 [8]}}