| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Modelling assumptions and refinements |
| Difficulty | Standard +0.3 This is a straightforward S1 question requiring systematic application of probability axioms (probabilities sum to 1) and expectation formulas. Part (a) involves setting up and solving simple linear equations, part (b) tests recognition of the discrete uniform distribution, and part (c) is a standard variance calculation. While multi-step, each component uses routine techniques with no novel insight required, making it slightly easier than average. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables5.02e Discrete uniform distribution |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\frac{1}{8} + 9p + 26q = 4.5\), \(\frac{1}{8} + 3p + 4q = 1\) | M1 A1 B1 | |
| \(9p + 26q = 4.375\), \(3p + 4q = 0.875\) | M1 M1 A1 A1 | |
| Solve: \(p = q = \frac{1}{8}\) | M1 M1 A1 A1 | |
| (b) Discrete uniform distribution | B1 | |
| (c) \(\frac{n^2-1}{12} = \frac{63}{12}\), s.d. = 2.29 | M1 A1 A1 | Total: 11 |
(a) $\frac{1}{8} + 9p + 26q = 4.5$, $\frac{1}{8} + 3p + 4q = 1$ | M1 A1 B1 |
$9p + 26q = 4.375$, $3p + 4q = 0.875$ | M1 M1 A1 A1 |
Solve: $p = q = \frac{1}{8}$ | M1 M1 A1 A1 |
(b) Discrete uniform distribution | B1 |
(c) $\frac{n^2-1}{12} = \frac{63}{12}$, s.d. = 2.29 | M1 A1 A1 | **Total: 11**The discrete random variable $X$ can take any value in the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$.
Arthur, Beatrice and Chris each carry out trials to investigate the distribution of $X$.
Arthur finds that P$(X = 1) = 0.125$ and that E$(X) = 4.5$.
Beatrice finds that P$(X = 2) =$ P$(X = 3) =$ P$(X = 4) = p$.
Chris finds that the values of $X$ greater than 4 are all equally likely, with each having probability $q$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the values of $p$ and $q$. [7 marks]
\item Give the name for the distribution of $X$. [1 mark]
\item Calculate the standard deviation of $X$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [11]}}