AQA Further AS Paper 2 Statistics 2020 June — Question 6

Exam BoardAQA
ModuleFurther AS Paper 2 Statistics (Further AS Paper 2 Statistics)
Year2020
SessionJune
TopicContinuous Probability Distributions and Random Variables
TypeFind median or percentiles

6 The continuous random variable \(X\) has probability density function $$f ( x ) = \left\{ \begin{array} { c c } \frac { 4 } { 45 } \left( x ^ { 3 } - 10 x ^ { 2 } + 29 x - 20 \right) & 1 \leq x \leq 4
0 & \text { otherwise } \end{array} \right.$$ 6
  1. Find \(\mathrm { P } ( X < 2 )\)
    6
  2. Verify that the median of \(X\) is 2.3 , correct to two significant figures.
    6
  3. Find the mean of \(X\).