| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | State or write down basic properties |
| Difficulty | Easy -1.3 This question tests basic definitions and properties of continuous uniform distributions with minimal calculation. Part (a) is pure recall of definitions, part (b) requires simple observation that 3 decimal places makes it discrete, and part (c) is a standard sketch of a linear CDF. All parts are routine bookwork with no problem-solving or multi-step reasoning required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams5.03a Continuous random variables: pdf and cdf5.03e Find cdf: by integration |
| Answer | Marks |
|---|---|
| (a) A discrete variable can only have certain values, usually integers | B1 |
| A continuous variable can take any value, often in a certain range | B1 |
| (b) \(X\) is continuous, but the calculator number is discrete, e.g. calculator cannot give 0.385721... | B1 |
| (c) Sketch: line from (0, 0) to (1, 1); on x-axis elsewhere | B2 |
(a) A discrete variable can only have certain values, usually integers | B1 |
A continuous variable can take any value, often in a certain range | B1 |
(b) $X$ is continuous, but the calculator number is discrete, e.g. calculator cannot give 0.385721... | B1 |
(c) Sketch: line from (0, 0) to (1, 1); on x-axis elsewhere | B2 |
**Total: 5 marks**
---\begin{enumerate}
\item (a) Explain the difference between a discrete and a continuous variable.
\end{enumerate}
A random number generator on a calculator generates numbers, $X$, to 3 decimal places, in the range 0 to 1 , e.g. 0.386 . The variable $X$ may be modelled by a continuous uniform distribution, having the probability density function $\mathrm { f } ( x )$, where
$$\begin{array} { l l }
\mathrm { f } ( x ) = 1 & 0 < x < 1 \\
\mathrm { f } ( x ) = 0 & \text { otherwise }
\end{array}$$
(b) Explain why this model is not totally accurate.\\
(c) Sketch the cumulative distribution function of $X$.\\
\hfill \mbox{\textit{Edexcel S2 Q1 [5]}}