| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Discrete Probability Distributions |
| Type | Conditional probability with random variables |
| Difficulty | Standard +0.3 This is a discrete probability distribution question requiring straightforward probability calculations. Part (a) is trivial substitution. Part (b) requires conditional probability with summation of an arithmetic series, which is standard S1 content but involves more steps than average, placing it slightly above typical difficulty. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
A random variable $X$ has probability distribution given by $P(X = x) = \frac{1}{860}(1 + x)$ for $x = 1, 2, 3, \ldots, 40$.
\begin{enumerate}[label=(\alph*)]
\item Find $P(X > 39)$. [2]
\item Given that $x$ is even, determine $P(X < 10)$. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2017 Q14 [8]}}