AQA S2 2013 January — Question 4

Exam BoardAQA
ModuleS2 (Statistics 2)
Year2013
SessionJanuary
TopicContinuous Probability Distributions and Random Variables
TypePiecewise PDF with multiple regions

4 A continuous random variable \(X\) has probability density function defined by $$f ( x ) = \begin{cases} k x ^ { 2 } & 0 \leqslant x \leqslant 3
9 k & 3 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
  1. Sketch the graph of f.
  2. Show that the value of \(k\) is \(\frac { 1 } { 18 }\).
    1. Write down the median value of \(X\).
    2. Calculate the value of the lower quartile of \(X\).