CAIE S1 2010 November — Question 2 5 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionNovember
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDiscrete Probability Distributions
TypeSimple algebraic expression for P(X=x)
DifficultyEasy -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.
Spec2.04a 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.
  1. Draw up a probability distribution table for \(X\), in terms of \(k\), and find the value of \(k\).
  2. Find \(\mathrm { E } ( X )\).

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]}}