OCR S2 2013 January — Question 4

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2013
SessionJanuary
TopicContinuous Probability Distributions and Random Variables
TypeSingle-piece PDF with k

4 A continuous random variable \(X\) has probability density function $$\mathrm { f } ( x ) = \left\{ \begin{array} { c l } k x & 0 \leqslant x \leqslant a
0 & \text { otherwise } \end{array} \right.$$ where \(k\) and \(a\) are constants.
  1. State what the letter \(x\) represents.
  2. Find \(k\) in terms of \(a\).
  3. Find \(\operatorname { Var } ( X )\) in terms of \(a\).