CAIE S2 2012 November — Question 7

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2012
SessionNovember
TopicPoisson Distribution
TypePoisson parameter from given probability

7 A random variable \(X\) has the distribution \(\operatorname { Po } ( 1.6 )\).
  1. The random variable \(R\) is the sum of three independent values of \(X\). Find \(\mathrm { P } ( R < 4 )\).
  2. The random variable \(S\) is the sum of \(n\) independent values of \(X\). It is given that $$\mathrm { P } ( S = 4 ) = \frac { 16 } { 3 } \times \mathrm { P } ( S = 2 )$$ Find \(n\).
  3. The random variable \(T\) is the sum of 40 independent values of \(X\). Find \(\mathrm { P } ( T > 75 )\).