Covariance calculation and independence

Questions asking to calculate Cov(X,Y) from a joint distribution and/or determine whether two random variables are independent.

1 questions

OCR S4 2010 June Q1
1 For the variables \(A\) and \(B\), it is given that \(\operatorname { Var } ( A ) = 9 , \operatorname { Var } ( B ) = 6\) and \(\operatorname { Var } ( 2 A - 3 B ) = 18\).
  1. Find \(\operatorname { Cov } ( A , B )\).
  2. State with a reason whether \(A\) and \(B\) are independent.