Edexcel S2 2013 June — Question 3

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2013
SessionJune
TopicContinuous Uniform Random Variables
TypeFind parameters from given statistics

3. The random variable \(X\) has a continuous uniform distribution on \([ a , b ]\) where \(a\) and \(b\) are positive numbers. Given that \(\mathrm { E } ( X ) = 23\) and \(\operatorname { Var } ( X ) = 75\)
  1. find the value of \(a\) and the value of \(b\). Given that \(\mathrm { P } ( X > c ) = 0.32\)
  2. find \(\mathrm { P } ( 23 < X < c )\).