Edexcel S2 2002 June — Question 3 9 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2002
SessionJune
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicContinuous Uniform Random Variables
TypeFind parameters from given statistics
DifficultyModerate -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.
Spec5.03b 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
  1. the value of \(\alpha\) and the value of \(\beta\), [7]
  2. \(\mathrm{P}(R < 6.6)\). [2]

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]}}