CAIE S2 2012 November — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2012
SessionNovember
TopicContinuous Probability Distributions and Random Variables
TypeFind parameter from probability condition

5 A random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} \frac { k } { x - 1 } & 3 \leqslant x \leqslant 5
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.
  1. Show that \(k = \frac { 1 } { \ln 2 }\).
  2. Find \(a\) such that \(\mathrm { P } ( X < a ) = 0.75\).