Edexcel S2 2018 January — Question 1

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2018
SessionJanuary
TopicCumulative distribution functions
TypeCalculate probabilities from CDF

  1. A continuous random variable \(X\) has cumulative distribution function
$$\mathrm { F } ( x ) = \left\{ \begin{array} { l r } 0 & x < 1
\frac { 1 } { 16 } ( x - 1 ) ^ { 2 } & 1 \leqslant x \leqslant 5
1 & x > 5 \end{array} \right.$$
  1. Find \(\mathrm { P } ( X > 4 )\)
  2. Find \(\mathrm { P } ( X > 3 \mid 2 < X < 4 )\)
  3. Find the exact value of \(\mathrm { E } ( X )\)