| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2019 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Random Variables |
| Type | Linear combinations of independent variables |
| Difficulty | Easy -1.2 This is a straightforward application of standard results for linear combinations of random variables (E(aX+b) and Var(aX+b)) with no problem-solving required. Both parts involve direct substitution into formulas that students learn by rote, making it easier than average. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(9.6, \ 12.4\) | B1 B1 | |
| 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(6.6, \ 49.6\) | B1 B1 | |
| 2 |
**Question 1:**
**Part (i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $9.6, \ 12.4$ | B1 B1 | |
| | **2** | |
**Part (ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $6.6, \ 49.6$ | B1 B1 | |
| | **2** | |
---1 The random variable $X$ has mean 2.4 and variance 3.1.\\
(i) The random variable $Y$ is the sum of four independent values of $X$. Find the mean and variance of $Y$.\\
(ii) The random variable $Z$ is defined by $Z = 4 X - 3$. Find the mean and variance of $Z$.\\
\hfill \mbox{\textit{CAIE S2 2019 Q1 [4]}}