| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2021 |
| Session | March |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Type | Geometric/graphical PDF with k |
| Difficulty | Standard +0.3 This is a straightforward S2 question requiring integration of a piecewise linear PDF. Part (a) uses the standard property that total area = 1 to find k (simple geometry/integration). Part (b) requires writing the PDF formula and computing E(X) using standard integration. Part (c) involves setting up and solving an integral equation. All techniques are routine for S2 with no novel insight required, making it slightly easier than average. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03f Relate pdf-cdf: medians and percentiles |
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\includegraphics[max width=\textwidth, alt={}, center]{2fefee17-50bb-4375-80f6-7e4bc2606492-04_405_789_260_676}
The diagram shows the graph of the probability density function, f , of a random variable $X$.
\begin{enumerate}[label=(\alph*)]
\item Find the value of the constant $k$.
\item Using this value of $k$, find $\mathrm { f } ( x )$ for $0 \leqslant x \leqslant k$ and hence find $\mathrm { E } ( X )$.
\item Find the value of $p$ such that $\mathrm { P } ( p < X < 1 ) = 0.25$.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2021 Q2 [9]}}