| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Arithmetic sequence uniform distribution |
| Difficulty | Moderate -0.8 This is a straightforward discrete uniform distribution question requiring only recall of standard formulas. Part (a) asks for a basic modelling assumption (equal probability), while part (b) involves direct application of E(X) and Var(X) formulas for uniform distributions with minimal calculation complexity. The 6-mark allocation reflects routine bookwork rather than problem-solving. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02e Discrete uniform distribution |
| Answer | Marks |
|---|---|
| (a) All cards are equally likely to be drawn | B1 |
| (b) \(E(X) = 31\) | M1 A1 M1 A1 A1 |
| \(\text{Var}(X) = 4 \times \frac{30^2-1}{12} = 299\frac{2}{3}\) | 6 marks total |
(a) All cards are equally likely to be drawn | B1 |
(b) $E(X) = 31$ | M1 A1 M1 A1 A1 |
$\text{Var}(X) = 4 \times \frac{30^2-1}{12} = 299\frac{2}{3}$ | 6 marks total |Thirty cards, marked with the even numbers from 2 to 60 inclusive, are shuffled and one card is withdrawn at random and then replaced. The random variable $X$ takes the value of the number on the card each time the experiment is repeated.
\begin{enumerate}[label=(\alph*)]
\item What must be assumed about the cards if the distribution of $X$ is modelled by a discrete uniform distribution? [1 mark]
\item Making this modelling assumption, find the expectation and the variance of $X$. [5 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q1 [6]}}