OCR S2 2007 June — Question 7

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2007
SessionJune
TopicContinuous Uniform Random Variables
TypeCompare uniform with other distributions

7 Two continuous random variables \(S\) and \(T\) have probability density functions as follows. $$\begin{array} { l l } S : & f ( x ) = \begin{cases} \frac { 1 } { 2 } & - 1 \leqslant x \leqslant 1
0 & \text { otherwise } \end{cases}
T : & g ( x ) = \begin{cases} \frac { 3 } { 2 } x ^ { 2 } & - 1 \leqslant x \leqslant 1
0 & \text { otherwise } \end{cases} \end{array}$$
  1. Sketch on the same axes the graphs of \(y = \mathrm { f } ( x )\) and \(y = \mathrm { g } ( x )\). [You should not use graph paper or attempt to plot points exactly.]
  2. Explain in everyday terms the difference between the two random variables.
  3. Find the value of \(t\) such that \(\mathrm { P } ( T > t ) = 0.2\).