CAIE S2 Specimen — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
SessionSpecimen
TopicContinuous Probability Distributions and Random Variables
TypeSingle-piece PDF with k
4 A random variable \(X\) has probability density function given by $$\mathrm { f } ( x ) = \begin{cases} k ( 3 - x ) & 1 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.
  1. Show that \(k = \frac { 2 } { 3 }\).
  2. Find the median of \(X\).
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