| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Simple algebraic expression for P(X=x) |
| Difficulty | Easy -1.2 This is a straightforward probability distribution question requiring only basic recall: summing probabilities to equal 1 to find k, then applying the standard E(X) formula. The arithmetic is simple (summing 1+2+3+4+5=15) and no problem-solving insight is needed—just direct application of fundamental definitions from early statistics. |
| Spec | 2.04a Discrete probability distributions5.02b Expectation and variance: discrete random variables |
2 In a probability distribution the random variable $X$ takes the value $x$ with probability $k x$, where $x$ takes values $1,2,3,4,5$ only.\\
(i) Draw up a probability distribution table for $X$, in terms of $k$, and find the value of $k$.\\
(ii) Find $\mathrm { E } ( X )$.
\hfill \mbox{\textit{CAIE S1 2010 Q2 [5]}}