| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2002 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Find parameters from given statistics |
| Difficulty | Moderate -0.3 This is a straightforward application of standard uniform distribution formulas. Students need to recall E(R) = (α+β)/2 and Var(R) = (β-α)²/12, then solve two simultaneous equations. Part (b) is routine probability calculation. While it requires algebraic manipulation, it's a textbook exercise with no novel insight needed, making it slightly easier than average. |
| Spec | 5.03b Solve problems: using pdf |
The continuous random variable $R$ is uniformly distributed on the interval $\alpha \leq R \leq \beta$. Given that $\mathrm{E}(R) = 3$ and $\mathrm{Var}(R) = \frac{25}{3}$, find
\begin{enumerate}[label=(\alph*)]
\item the value of $\alpha$ and the value of $\beta$, [7]
\item $\mathrm{P}(R < 6.6)$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2002 Q3 [9]}}