| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2016 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Calculate E(X) from constructed distribution |
| Difficulty | Moderate -0.8 This is a straightforward probability distribution question requiring systematic enumeration of outcomes (6×6=36 cases), constructing the distribution for differences 0-5, then applying the standard E(X) formula. It's computational rather than conceptually challenging, making it easier than average but not trivial due to the enumeration work required. |
| Spec | 5.02b Expectation and variance: discrete random variables |
| Answer | Marks | Guidance |
|---|---|---|
| diff | 0 | 1 |
| prob | 6/36 | 10/36 |
| B1 | 0, 1, 2, 3, 4, 5 seen in table heading or considering all different differences | |
| M1 | Attempt at finding prob of any difference | |
| A1 | 1 correct prob | |
| M1 | Probs summing to 1 |
| Answer | Marks |
|---|---|
| A1 | [5] |
**diff** | 0 | 1 | 2 | 3 | 4 | 5
**prob** | 6/36 | 10/36 | 8/36 | 6/36 | 4/36 | 2/36
B1 | 0, 1, 2, 3, 4, 5 seen in table heading or considering all different differences
M1 | Attempt at finding prob of any difference
A1 | 1 correct prob
M1 | Probs summing to 1
Expectation $= \frac{0+10+16+18+16+10}{36} = \frac{70}{36} = 1.94$
A1 | [5]
---2 Two fair six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 are thrown and the two scores are noted. The difference between the two scores is defined as follows.
\begin{itemize}
\item If the scores are equal the difference is zero.
\item If the scores are not equal the difference is the larger score minus the smaller score.
\end{itemize}
Find the expectation of the difference between the two scores.
\hfill \mbox{\textit{CAIE S1 2016 Q2 [5]}}