CAIE FP2 2018 June — Question 6

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2018
SessionJune
TopicCumulative distribution functions
TypeInterquartile range calculation

6 The continuous random variable \(X\) has distribution function given by $$\mathrm { F } ( x ) = \begin{cases} 1 - \mathrm { e } ^ { - 0.4 x } & x \geqslant 0
0 & \text { otherwise } \end{cases}$$
  1. Find \(\mathrm { P } ( X > 2 )\).
  2. Find the interquartile range of \(X\).