OCR Further Statistics 2021 November — Question 8

Exam BoardOCR
ModuleFurther Statistics (Further Statistics)
Year2021
SessionNovember
TopicContinuous Uniform Random Variables
TypeTranscendental function expectations

8 The continuous random variable \(Y\) has a uniform distribution on [0,2].
  1. It is given that \(\mathrm { E } [ a \cos ( a Y ) ] = 0.3\), where \(a\) is a constant between 0 and 1 , and \(a Y\) is measured in radians. Determine the value of the constant \(a\).
  2. Determine the \(60 ^ { \text {th } }\) percentile of \(Y ^ { 2 }\).