| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Probability distribution from formula |
| Difficulty | Moderate -0.3 This is a straightforward discrete probability distribution question requiring basic substitution and table construction. Part (i) is simple verification, parts (ii-iii) involve routine calculations and identifying the mode, and part (iv) requires adding probabilities. The arithmetic is slightly tedious but conceptually this is below average difficulty for A-level, requiring only basic probability distribution understanding with no problem-solving insight. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
5 In a particular discrete probability distribution the random variable $X$ takes the value $\frac { 120 } { r }$ with probability $\frac { r } { 45 }$, where $r$ takes all integer values from 1 to 9 inclusive.\\
(i) Show that $\mathrm { P } ( X = 40 ) = \frac { 1 } { 15 }$.\\
(ii) Construct the probability distribution table for $X$.\\
(iii) Which is the modal value of $X$ ?\\
(iv) Find the probability that $X$ lies between 18 and 100 .
\hfill \mbox{\textit{CAIE S1 2009 Q5 [8]}}