| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | State or write down basic properties |
| Difficulty | Easy -1.2 This is a straightforward application of the continuous uniform distribution with minimal conceptual challenge. Part (a) requires simple recognition that X ~ U(0, 360), and part (b) involves direct substitution into standard formulas for mean and variance of a uniform distribution—purely routine recall with no problem-solving or insight required. |
| Spec | 5.02e Discrete uniform distribution |
| Answer | Marks |
|---|---|
| (a) Continuous uniform distribution on \([0, 360]\) | B1 |
| (b) Mean \(= 180\), s.d. \(= \sqrt{360^2 + 12} = \sqrt{10800} = 103.9\) | B1 M1 A1 |
(a) Continuous uniform distribution on $[0, 360]$ | B1 |
(b) Mean $= 180$, s.d. $= \sqrt{360^2 + 12} = \sqrt{10800} = 103.9$ | B1 M1 A1 |
**Total: 4 marks**
---A searchlight is rotating in a horizontal circle. It is assumed that that, at any moment, the centre of its beam is equally likely to be pointing in any direction. The random variable $X$ represents this direction, expressed as a bearing in the range $000°$ to $360°$.
\begin{enumerate}[label=(\alph*)]
\item Specify a suitable model for the distribution of $X$. [1 mark]
\item Find the mean and the standard deviation of $X$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q2 [4]}}