| Exam Board | WJEC |
|---|---|
| Module | Further Unit 2 (Further Unit 2) |
| Year | 2019 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Type | Expectation of function of X |
| Difficulty | Standard +0.3 This is a standard Further Maths probability question requiring integration to find k, E(X), and using linear transformation properties. The piecewise function adds mild complexity, but the techniques are routine: integrating polynomials and applying standard variance/expectation formulas. Slightly above average due to the piecewise nature and being Further Maths content, but still a textbook exercise. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | Jul-Sept | 200 |
Question 4:
4 | Jul-Sept | 200 | 217.254. The continuous random variable, $X$, has the following probability density function
$$f ( x ) = \begin{cases} k x & \text { for } 0 \leqslant x < 1 \\ k x ^ { 3 } & \text { for } 1 \leqslant x \leqslant 2 \\ 0 & \text { otherwise } \end{cases}$$
where $k$ is a constant.\\
\includegraphics[max width=\textwidth, alt={}, center]{4ecf99c5-c4b3-41b7-a8df-a7c2ca7fcd6a-3_851_935_826_678}
\begin{enumerate}[label=(\alph*)]
\item Show that $k = \frac { 4 } { 17 }$.
\item Determine $\mathrm { E } ( X )$.
\item Calculate $\mathrm { E } ( 3 X - 1 )$ and $\operatorname { Var } ( 3 X - 1 )$.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 2 2019 Q4 [15]}}