| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Find parameter from variance or other constraint |
| Difficulty | Standard +0.3 This question tests standard formulas for discrete uniform distribution (mean and variance) and basic probability calculation. While it requires knowing the variance formula σ²=(n²-1)/12 and solving a quadratic equation, these are routine S1 techniques with straightforward algebraic manipulation. The probability calculation in part (b) is direct counting once n is found. |
| Spec | 5.02c Linear coding: effects on mean and variance5.02e Discrete uniform distribution |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\frac{n^2 - 1}{12} = 24\) giving \(n = 17\); \(E(X) = 9\) | M1 A1 A1 | |
| (b) \(P(3 \leq X < 8 \cdot 5) = P(X = 3, 4, 5, 6, 7 \text{ or } 8) = \frac{6}{17}\) | M1 M1 A1 | Total: 6 marks |
(a) $\frac{n^2 - 1}{12} = 24$ giving $n = 17$; $E(X) = 9$ | M1 A1 A1 |
(b) $P(3 \leq X < 8 \cdot 5) = P(X = 3, 4, 5, 6, 7 \text{ or } 8) = \frac{6}{17}$ | M1 M1 A1 | Total: 6 marksThe random variable $X$ has the discrete uniform distribution and takes the values $\{1, \ldots, n\}$.
The standard deviation of of $X$ is $2\sqrt{6}$. Find
\begin{enumerate}[label=(\alph*)]
\item the mean of $X$, [3 marks]
\item P$(3 \leq X < \frac{2}{5}n)$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [6]}}