CAIE FP2 2017 November — Question 7

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2017
SessionNovember
TopicExponential Distribution
TypeDerive CDF from PDF

7 The random variable \(X\) has probability density function f given by $$\mathrm { f } ( x ) = \begin{cases} 0.2 \mathrm { e } ^ { - 0.2 x } & x \geqslant 0
0 & \text { otherwise } \end{cases}$$
  1. Find the distribution function of \(X\).
  2. Find \(\mathrm { P } ( X > 2 )\).
  3. Find the median of \(X\).