Normal linear combinations

• All linear combinations of independent normal variables is also normally distributed.
• E(aX ± bY + c) = aE(X) ± bE(Y) + c

  Var(aX ± bY + c) = a2 Var(X) + b2 Var(Y)
• Addition or multiplication?


  • When we need multiple of the same thing we add (pack of biscuits)
  • When we need to change the size we multiply (big biscuit)
• Subtraction trick


  If we are asked if one distribution is greater than another (a>b) we use the subtraction trick of b-a > 0 to find the answer.