| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2017 |
| Session | January |
| Marks | 7 |
| 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 recalling E(X) = (α+β)/2, part (b) involves simple linear equations, and parts (c)-(d) use standard variance and probability formulas. All steps are routine with no problem-solving insight required, making it easier than average but not trivial since it requires knowing multiple formulas and careful arithmetic across four parts. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration |
2. The continuous random variable $X$ is uniformly distributed over the interval $[ \alpha , \beta ]$ where $\beta > \alpha$
Given that $\mathrm { E } ( X ) = 8$
\begin{enumerate}[label=(\alph*)]
\item write down an equation involving $\alpha$ and $\beta$
Given also that $\mathrm { P } ( X \leqslant 13 ) = 0.7$
\item find the value of $\alpha$ and the value of $\beta$
\item find $\operatorname { Var } ( X )$
\item find $\mathrm { P } ( 5 \leqslant X \leqslant 35 )$
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2017 Q2 [7]}}