OCR S4 2009 June — Question 4

Exam BoardOCR
ModuleS4 (Statistics 4)
Year2009
SessionJune
TopicProbability Generating Functions
TypeSolve for parameters using PGF coefficients

4 The probability generating function of the discrete random variable \(Y\) is given by $$\mathrm { G } _ { Y } ( t ) = \frac { a + b t ^ { 3 } } { t }$$ where \(a\) and \(b\) are constants.
  1. Given that \(\mathrm { E } ( Y ) = - 0.7\), find the values of \(a\) and \(b\).
  2. Find \(\operatorname { Var } ( Y )\).
  3. Find the probability that the sum of 10 random observations of \(Y\) is - 7 .