CAIE S2 2004 November — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2004
SessionNovember
TopicContinuous Probability Distributions and Random Variables
TypeCalculate probability P(X in interval)
6 A continuous random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} 3 ( 1 - x ) ^ { 2 } & 0 \leqslant x \leqslant 1
0 & \text { otherwise } \end{cases}$$ Find
  1. \(\mathrm { P } ( X > 0.5 )\),
  2. the mean and variance of \(X\).
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