CAIE FP2 2013 June — Question 6

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionJune
TopicExponential Distribution
TypeState distribution and mean

6 The random variable \(X\) has distribution function F given by $$\mathrm { F } ( x ) = \begin{cases} 1 - \mathrm { e } ^ { - 0.6 x } & x \geqslant 0
0 & \text { otherwise } \end{cases}$$ Identify the distribution of \(X\) and state its mean. Find
  1. \(\mathrm { P } ( X > 4 )\),
  2. the median of \(X\).