CAIE S2 2013 June — Question 2

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2013
SessionJune
TopicContinuous Probability Distributions and Random Variables
TypeCompare mean and median using probability

2 A random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} \frac { 2 } { 3 } x & 1 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$
  1. Find \(\mathrm { E } ( X )\).
  2. Find \(\mathrm { P } ( X < \mathrm { E } ( X ) )\).
  3. Hence explain whether the mean of \(X\) is less than, equal to or greater than the median of \(X\).