| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2003 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Basic E(X) and Var(X) calculation |
| Difficulty | Easy -1.3 This is a straightforward application of binomial distribution formulas (mean = np, variance = np(1-p)) with p=0.5, n=5, followed by applying the linear transformation rules E(aX) = aE(X) and Var(aX) = a²Var(X). Requires only direct recall and substitution with no problem-solving or conceptual challenge. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Mean: \(2.5\) | \(B1\) | For correct mean |
| Variance: \(1.25\) | \(B1\) | For correct variance |
| (ii) Mean: \(5\) | \(B1ft\) | For correct mean |
| Variance: \(5\) | \(B1ft\) | For correct variance |
**(i)** Mean: $2.5$ | $B1$ | For correct mean
Variance: $1.25$ | $B1$ | For correct variance
**(ii)** Mean: $5$ | $B1ft$ | For correct mean
Variance: $5$ | $B1ft$ | For correct variance1 A fair coin is tossed 5 times and the number of heads is recorded.\\
(i) The random variable $X$ is the number of heads. State the mean and variance of $X$.\\
(ii) The number of heads is doubled and denoted by the random variable $Y$. State the mean and variance of $Y$.
\hfill \mbox{\textit{CAIE S2 2003 Q1 [4]}}