OCR S2 2011 June — Question 4

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2011
SessionJune
TopicContinuous Probability Distributions and Random Variables
TypeDirect variance calculation from pdf

4 A continuous random variable \(X\) has probability density function $$f ( x ) = \begin{cases} \frac { 3 } { 16 } ( x - 2 ) ^ { 2 } & 0 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
  1. Sketch the graph of \(y = \mathrm { f } ( x )\).
  2. Calculate the variance of \(X\).
  3. A student writes " \(X\) is more likely to occur when \(x\) takes values further away from 2 ". Explain whether you agree with this statement.