AQA S2 2007 January — Question 8

Exam BoardAQA
ModuleS2 (Statistics 2)
Year2007
SessionJanuary
TopicCumulative distribution functions
TypeCDF to PDF derivation

8 The continuous random variable \(X\) has the cumulative distribution function $$\mathrm { F } ( x ) = \left\{ \begin{array} { c c } 0 & x \leqslant - 4
\frac { x + 4 } { 9 } & - 4 \leqslant x \leqslant 5
1 & x \geqslant 5 \end{array} \right.$$
  1. Determine the probability density function, \(\mathrm { f } ( x )\), of \(X\).
  2. Sketch the graph of f .
  3. Determine \(\mathrm { P } ( X > 2 )\).
  4. Evaluate the mean and variance of \(X\).