| 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 straightforward question testing basic understanding of continuous uniform distributions. Part (i) requires only applying the fundamental property that the total area under a PDF equals 1 (rectangle area = base × height = 20k = 1, so k = 0.05). Part (ii) is a simple interpretation requiring no calculation. Both parts are routine recall with minimal problem-solving. |
| Spec | 5.03a Continuous random variables: pdf and cdf |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{1}{12}\) | B1 [1] | Accept 0.0833 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Trains arrive every 12 minutes | B1 [1] | Must have 'every 12 minutes' |
## Question 1:
**(i)**
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{1}{12}$ | B1 [1] | Accept 0.0833 |
**(ii)**
| Answer | Mark | Guidance |
|--------|------|----------|
| Trains arrive every 12 minutes | B1 [1] | Must have 'every 12 minutes' |
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\includegraphics[max width=\textwidth, alt={}, center]{f73b303b-eb56-4c35-aa3e-388e3a3e8acd-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]}}