| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Type | Geometric/graphical PDF with k |
| Difficulty | Moderate -0.8 This is a straightforward PDF question requiring only basic integration and the fundamental property that total probability equals 1. Part (a) uses ∫f(x)dx = 1 to find p (likely a simple linear or constant function from the graph), and part (b) is a standard E(X) calculation. Both are routine textbook exercises with no problem-solving insight required. |
| 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]{189bcf7b-279f-457b-8232-ace7f0c9797f-05_456_668_260_735}
The random variable $X$ takes values in the range $1 \leqslant x \leqslant p$, where $p$ is a constant. The graph of the probability density function of $X$ is shown in the diagram.
\begin{enumerate}[label=(\alph*)]
\item Show that $p = 2$.
\item Find $\mathrm { E } ( X )$.
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2021 Q3 [7]}}