OCR Further Statistics Specimen — Question 9

Exam BoardOCR
ModuleFurther Statistics (Further Statistics)
SessionSpecimen
TopicCumulative distribution functions
TypeCDF of transformed variable

9 The continuous random variable \(X\) has cumulative distribution function given by $$\mathrm { F } ( x ) = \left\{ \begin{array} { c c } 0 & x < 0
\frac { 1 } { 16 } x ^ { 2 } & 0 \leq x \leq 4
1 & x > 4 \end{array} \right.$$
  1. The random variable \(Y\) is defined by \(Y = \frac { 1 } { X ^ { 2 } }\). Find the cumulative distribution function of \(Y\).
  2. Show that \(\mathrm { E } ( Y )\) is not defined. \section*{END OF QUESTION PAPER}