Transcendental function expectations

Questions involving E(g(X)) where g contains trigonometric, exponential, or other transcendental functions requiring specialized integration techniques or numerical methods.

1 questions · Challenging +1.8

5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration5.03f Relate pdf-cdf: medians and percentiles
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OCR Further Statistics 2021 November Q8
11 marks Challenging +1.8
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 \(Y ^ { 2 }\).