| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Find constant k in PDF |
| Difficulty | Easy -1.8 This is a very straightforward question requiring only recognition that the area under a PDF equals 1, leading to k × (base) = 1. Part (ii) requires basic interpretation of a uniform distribution. This is simpler than typical A-level questions as it involves minimal calculation and tests only fundamental PDF properties. |
| Spec | 5.03a Continuous random variables: pdf and cdf |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\frac{1}{12}\) | B1 [1] | Accept 0.0833 |
| (ii) trains arrive every 12 minutes | B1 [1] | must have 'every 12 minutes' |
**(i)** $\frac{1}{12}$ | B1 [1] | Accept 0.0833
**(ii)** trains arrive every 12 minutes | B1 [1] | must have 'every 12 minutes'1\\
\includegraphics[max width=\textwidth, alt={}, center]{29ab8740-9fad-4596-b34f-c424b5464858-2_453_1258_251_447}
Fred arrives at random times on a station platform. The times in minutes he has to wait for the next train are modelled by the continuous random variable for which the probability density function f is shown above.\\
(i) State the value of $k$.\\
(ii) Explain briefly what this graph tells you about the arrival times of trains.
\hfill \mbox{\textit{CAIE S2 2010 Q1 [2]}}