OCR H240/02 2017 Specimen — Question 14 8 marks

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2017
SessionSpecimen
Marks8
TopicDiscrete Probability Distributions
TypeConditional probability with random variables
DifficultyStandard +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.
Spec5.02a 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 \(x = 1, 2, 3, \ldots, 40\).
  1. Find \(P(X > 39)\). [2]
  2. Given that \(x\) is even, determine \(P(X < 10)\). [6]

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]}}