CAIE S2 2010 November — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2010
SessionNovember
TopicContinuous Probability Distributions and Random Variables
TypeFind expectation E(X)

5 A continuous random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} \frac { 1 } { 6 } x & 2 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
  1. Find \(\mathrm { E } ( X )\).
  2. Find the median of \(X\).
  3. Two independent values of \(X\) are chosen at random. Find the probability that both these values are greater than 3 .