| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Difficulty | Standard +0.3 This is a standard S2 question on piecewise probability density functions requiring routine integration and CDF calculation. While it has multiple parts and requires careful handling of the piecewise function, all techniques are straightforward applications of standard formulas 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 integration5.03e Find cdf: by integration |
The continuous random variable X has probability density function
$$f(x) = \begin{cases}
\frac{x}{15}, & 0 \leq x \leq 2, \\
\frac{x}{15}, & \\
\frac{2x}{45}, & 2 < x < 7, \\
\frac{2}{9}, & 7 \leq x \leq 10, \\
0, & otherwise.
\end{cases}$$
\begin{enumerate}[label=(\alph*)]
\item Sketch f(x) for all values of x. [3]
\item Find expressions for the cumulative distribution function, F(x), for 0 ≤ x ≤ 2 and for 7 ≤ x ≤ 10. [8]
\item Find P(X ≤ 8.2). [2]
\item Find, to 3 significant figures, E(X). [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q7 [17]}}