aX+b (Edexcel International AS Maths: Statistics 1)

How are the mean and variance of X related to the mean and variance of aX + b?

• If a and b are constants then the following results are true
  • E(aX + b) = aE(X) + b
  • Var(aX + b) = a² Var(X)
• Note that the mean is affected by multiplication and addition whereas addition does not change the variance
• The factor of a²  includes the squared because the values of X are squared in the calculation
  • You could try and use the first result and the formula for variance to verify the second result
• Remember a subtraction can be written as an addition
  • X – b can be written as X + (-b)
• And division can be written as a multiplication
  • can be written as