| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Type | Find expectation E(X) |
| Difficulty | Standard +0.3 This is a straightforward application of the expectation formula for a piecewise continuous PDF requiring integration over two intervals. The integrals are routine (polynomial and square root functions), and part (ii) simply requires evaluating a probability using the given PDF. Standard S3 material with no conceptual challenges beyond careful arithmetic. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf |
1 A continuous random variable $X$ has probability density function given by
$$f ( x ) = \begin{cases} \frac { 2 x } { 5 } & 0 \leqslant x \leqslant 1 \\ \frac { 2 } { 5 \sqrt { x } } & 1 < x \leqslant 4 \\ 0 & \text { otherwise } \end{cases}$$
Find\\
(i) $\mathrm { E } ( X )$,\\
(ii) $\mathrm { P } ( X \geqslant \mathrm { E } ( X ) )$.
\hfill \mbox{\textit{OCR S3 2009 Q1 [6]}}