CAIE FP2 2019 June — Question 7

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2019
SessionJune
TopicCumulative distribution functions
TypePDF to CDF derivation

7 The continuous random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} \frac { 3 } { 4 x ^ { 2 } } + \frac { 1 } { 4 } & 1 \leqslant x \leqslant 3
0 & \text { otherwise } \end{cases}$$
  1. Find the distribution function of \(X\).
  2. Find the exact value of the interquartile range of \(X\).