OCR S3 2009 January — Question 2

Exam BoardOCR
ModuleS3 (Statistics 3)
Year2009
SessionJanuary
TopicCumulative distribution functions
TypeCDF to PDF derivation

2 The continuous random variable \(U\) has (cumulative) distribution function given by $$\mathrm { F } ( u ) = \begin{cases} \frac { 1 } { 5 } \mathrm { e } ^ { u } & u < 0
1 - \frac { 4 } { 5 } \mathrm { e } ^ { - \frac { 1 } { 4 } u } & u \geqslant 0 \end{cases}$$
  1. Find the upper quartile of \(U\).
  2. Find the probability density function of \(U\).