| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2020 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Type | Geometric/graphical PDF with k |
| Difficulty | Moderate -0.3 This is a straightforward S2 PDF question requiring standard techniques: using the area-under-curve property to find c, calculating a probability as an area (likely a trapezium or triangle), and computing E(X) by integration. While it involves multiple parts, each step follows routine procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration |
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\includegraphics[max width=\textwidth, alt={}, center]{4a5f9f7e-b045-4c6f-8bda-6c4067668da2-04_332_1100_260_520}
A random variable $X$ takes values between 0 and 3 only and has probability density function as shown in the diagram, where $c$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Show that $c = \frac { 2 } { 3 }$.
\item Find $\mathrm { P } ( X > 2 )$.
\item Calculate $\mathrm { E } ( X )$.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2020 Q3 [7]}}