Edexcel S2 2015 June — Question 5

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2015
SessionJune
TopicDiscrete Random Variables
TypeSampling distribution of mean or linear combination

5. A bag contains a large number of counters with \(35 \%\) of the counters having a value of 6 and \(65 \%\) of the counters having a value of 9 A random sample of size 2 is taken from the bag and the value of each counter is recorded as \(X _ { 1 }\) and \(X _ { 2 }\) respectively. The statistic \(Y\) is calculated using the formula $$Y = \frac { 2 X _ { 1 } + X _ { 2 } } { 3 }$$
  1. List all the possible values of \(Y\).
  2. Find the sampling distribution of \(Y\).
  3. Find \(\mathrm { E } ( Y )\).