| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2020 |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Difficulty | Standard +0.3 This is a straightforward probability density function question requiring standard techniques: reading values from a given diagram for parts (a) and (b), and using the complement rule with given information for part (c). The 'state' command indicates values should be directly readable from the diagram rather than calculated, making this easier than typical PDF questions. While it involves multiple parts, each requires only basic probability concepts with minimal calculation. |
| Spec | 5.03c Calculate mean/variance: by integration |
The diagram shows the graph of the probability density function of a random variable $X$, where
$$f(x) = \begin{cases}
\frac{1}{6}(3x - x^2) & 0 \leq x \leq 3, \\
0 & \text{otherwise}.
\end{cases}$$
\includegraphics{figure_1}
\begin{enumerate}[label=(\alph*)]
\item State the values of E($X$) and Var($X$). [4]
\item State the values of P($0.5 < X < 1$). [1]
\item Given that P($1 < X < 2$) = $\frac{13}{27}$, find P($X > 2$). [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2020 Q5 [7]}}