Edexcel S2 2013 June — Question 4

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2013
SessionJune
TopicContinuous Uniform Random Variables
TypeDerive or verify variance formula
  1. A continuous random variable \(X\) is uniformly distributed over the interval [ \(b , 4 b\) ] where \(b\) is a constant.
    1. Write down \(\mathrm { E } ( X )\).
    2. Use integration to show that \(\operatorname { Var } ( X ) = \frac { 3 b ^ { 2 } } { 4 }\).
    3. Find \(\operatorname { Var } ( 3 - 2 X )\).
    Given that \(b = 1\) find
  2. the cumulative distribution function of \(X , \mathrm {~F} ( x )\), for all values of \(x\),
  3. the median of \(X\).
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