| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Breaking/cutting problems |
| Difficulty | Moderate -0.8 This is a straightforward application of continuous uniform distribution requiring students to identify the model (U(0,12)), derive its CDF using standard integration, and read off a probability. All steps are routine S2 content with no problem-solving insight needed, making it easier than average but not trivial due to the CDF derivation requirement. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03e Find cdf: by integration |
A piece of string $AB$ has length 12 cm. A child cuts the string at a randomly chosen point $P$, into two pieces. The random variable $X$ represents the length, in cm, of the piece $AP$.
\begin{enumerate}[label=(\alph*)]
\item Suggest a suitable model for the distribution of $X$ and specify it fully [2]
\item Find the cumulative distribution function of $X$. [4]
\item Write down P($X < 4$). [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q2 [7]}}