| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Find parameters from given statistics |
| Difficulty | Standard +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. The algebra is routine (solving α+β=6 and (β-α)²=16), and part (b) is a simple probability calculation. Slightly above average difficulty due to the algebraic manipulation required, but still a standard textbook exercise with no novel insight needed. |
| Spec | 5.02e Discrete uniform distribution5.03c Calculate mean/variance: by integration |
The continuous random variable R is uniformly distributed on the interval $\alpha \leq R \leq \beta$. Given that E(R) = 3 and Var(R) = $\frac{4}{3}$, find
\begin{enumerate}[label=(\alph*)]
\item the value of $\alpha$ and the value of $\beta$, [7]
\item P(R < 6.6). [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q3 [9]}}