Edexcel S2 — Question 3 9 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Marks9
PaperDownload PDF ↗
TopicContinuous Uniform Random Variables
TypeFind parameters from given statistics
DifficultyStandard +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.
Spec5.02e 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
  1. the value of \(\alpha\) and the value of \(\beta\), [7]
  2. P(R < 6.6). [2]

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]}}