| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2016 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Cumulative distribution functions |
| Type | Uniform distribution transformations |
| Difficulty | Challenging +1.2 This question requires transforming a uniform distribution using the function A = 4πR², finding both CDF and PDF through the transformation method, then applying the result. While it involves multiple steps and the transformation of random variables (a Further Maths S3 topic), the approach is methodical and follows standard procedures taught in the specification. The calculation itself is straightforward once the method is recalled. |
| Spec | 5.03g Cdf of transformed variables |
8 The radius, $R$, of a sphere is a random variable with a continuous uniform distribution between 0 and 10 .\\
(i) Find the cumulative distribution function and probability density function of $A$, the surface area of the sphere.\\
(ii) Find $\mathrm { P } ( \mathrm { A } \leqslant 200 \pi )$.
\section*{END OF QUESTION PAPER}
\hfill \mbox{\textit{OCR S3 2016 Q8 [10]}}