aX+b
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 
