CAIE FP2 2011 June — Question 5

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2011
SessionJune
TopicExponential Distribution
TypeState distribution and mean

5 The continuous random variable \(X\) has probability density function f given by $$\mathrm { f } ( x ) = \begin{cases} 0.01 \mathrm { e } ^ { - 0.01 x } & x \geqslant 0
0 & x < 0 \end{cases}$$
  1. State the value of \(\mathrm { E } ( X )\).
  2. Find the median value of \(X\).
  3. Find the probability that \(X\) lies between the median and the mean.