| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2020 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Find parameters from given statistics |
| Difficulty | Moderate -0.5 This is a straightforward continuous uniform distribution question requiring basic recall of standard formulas. Part (a) uses the fundamental property that total probability equals 1 (giving k=1/a), and part (b) applies the standard variance formula for uniform distributions. While it involves algebraic manipulation, it requires no problem-solving insight beyond direct application of textbook formulas, making it slightly easier than average. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03c Calculate mean/variance: by integration |
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\includegraphics[max width=\textwidth, alt={}, center]{fb305858-2d96-4a5d-b1a9-a965c248fb8d-07_316_984_260_577}
The diagram shows the probability density function, $\mathrm { f } ( x )$, of a random variable $X$. For $0 \leqslant x \leqslant a$, $\mathrm { f } ( x ) = k$; elsewhere $\mathrm { f } ( x ) = 0$.
\begin{enumerate}[label=(\alph*)]
\item Express $k$ in terms of $a$.
\item Given that $\operatorname { Var } ( X ) = 3$, find $a$.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2020 Q4 [5]}}