| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | E(g(X)) and Var(g(X)) by integration |
| Difficulty | Standard +0.3 This is a straightforward continuous uniform distribution question requiring basic integration. Part (i) uses the fundamental property that pdf integrates to 1 (trivial for uniform). Part (ii) requires computing E(g(X)) = ∫400√x·(1/20)dx over [25,45], which is routine integration of x^(1/2). Part (iii) involves solving an inequality and finding a probability from the uniform distribution. All steps are standard S3 techniques with no conceptual challenges, 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 integration |
4 The weekly sales of petrol, $X$ thousand litres, at a garage may be modelled by a continuous random variable with probability density function given by
$$f ( x ) = \begin{cases} c & 25 \leqslant x \leqslant 45 \\ 0 & \text { otherwise } \end{cases}$$
where $c$ is a constant. The weekly profit, in $\pounds$, is given by $( 400 \sqrt { X } - 240 )$.\\
(i) Obtain the value of $c$.\\
(ii) Find the expected weekly profit.\\
(iii) Find the probability that the weekly profit exceeds $\pounds 2000$.
\hfill \mbox{\textit{OCR S3 2009 Q4 [7]}}