| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Find parameters from given statistics |
| Difficulty | Moderate -0.8 This is a straightforward application of standard uniform distribution formulas. Part (a) requires knowing that mean = (a+b)/2 to find n, then applying the variance formula. Part (b) is a simple probability calculation using the uniform pdf. All steps are direct formula application with no problem-solving insight required, making it easier than average. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration |
| Answer | Marks |
|---|---|
| (a) \((n+1)/2 = 12\) so \(n = 23\); \(\text{Var}(X) = \frac{(23-1)^2}{12} = 40\frac{1}{3}\) | B1 M1 A1; M1 A1 |
| (b) \(P(10 < X < 14) = \frac{4}{22} = \frac{2}{11}\) |
(a) $(n+1)/2 = 12$ so $n = 23$; $\text{Var}(X) = \frac{(23-1)^2}{12} = 40\frac{1}{3}$ | B1 M1 A1; M1 A1 |
(b) $P(10 < X < 14) = \frac{4}{22} = \frac{2}{11}$ | |
**Total: 5 marks**
---2. The random variable $X$, which can take any value in the interval $1 \leq X \leq n$, is modelled by the continuous uniform distribution with mean 12.
\begin{enumerate}[label=(\alph*)]
\item Show that $n = 23$ and find the variance of $X$.
\item Find $\mathrm { P } ( 10 < X < 14 )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q2 [5]}}