CAIE FP2 2018 November — Question 6

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2018
SessionNovember
TopicContinuous Probability Distributions and Random Variables
TypeSquare root transformation (Y = √X)

6 The continuous random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} \frac { 1 } { 80 } \left( 3 \sqrt { } x - \frac { 8 } { \sqrt { } x } \right) & 4 \leqslant x \leqslant 16
0 & \text { otherwise } \end{cases}$$
  1. Find the distribution function of \(X\).
    The random variable \(Y\) is defined by \(Y = \sqrt { } X\).
  2. Find the probability density function of \(Y\).