| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Breaking/cutting problems |
| Difficulty | Moderate -0.3 This is a straightforward continuous uniform distribution problem requiring identification of the distribution, sketching a simple pdf, and calculating a probability using geometric reasoning. While it requires understanding of continuous distributions and careful thinking about the 'longer part' constraint, the mathematics involved is routine for S2 level with no complex integration or novel problem-solving required. |
| Spec | 5.02e Discrete uniform distribution5.03a Continuous random variables: pdf and cdf |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Continuous uniform \(U[15, 30]\) Graph drawn | B2 B2 | |
| (b) \(P(X > 20) = \frac{10}{15} = \frac{2}{3}\) | M1 A1 A1 | Total: 7 marks |
(a) Continuous uniform $U[15, 30]$ Graph drawn | B2 B2 |
(b) $P(X > 20) = \frac{10}{15} = \frac{2}{3}$ | M1 A1 A1 | **Total: 7 marks**A child cuts a 30 cm piece of string into two parts, cutting at a random point.
\begin{enumerate}[label=(\alph*)]
\item Name the distribution of $L$, the length of the longer part of string, and sketch the
probability density function for $L$. [4 marks]
\item Find the probability that one part of the string is more than twice as long as the other. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q3 [7]}}