Edexcel S2 2008 January — Question 8

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2008
SessionJanuary
TopicContinuous Probability Distributions and Random Variables
TypeCalculate and compare mean, median, mode

  1. The continuous random variable \(X\) has probability density function \(\mathrm { f } ( x )\) given by
$$f ( x ) = \left\{ \begin{array} { c c } 2 ( x - 2 ) & 2 \leqslant x \leqslant 3
0 & \text { otherwise } \end{array} \right.$$
  1. Sketch \(\mathrm { f } ( x )\) for all values of \(x\).
  2. Write down the mode of \(X\). Find
  3. \(\mathrm { E } ( X )\),
  4. the median of \(X\).
  5. Comment on the skewness of this distribution. Give a reason for your answer.