CAIE FP2 2017 June — Question 8

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2017
SessionJune
TopicContinuous Probability Distributions and Random Variables
TypePower transformation (Y = X^n, n≥2)

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