A-Level CAIE Mathematics A2 6.2.1—Normal distribution Question Bank

• use, when solving problems, the results that - E(aX + b) = aE(X) + b and Var(aX + b) = a2 Var(X) - E(aX + bY) = aE(X) + bE(Y) - Var(aX + bY) = a2 Var(X) + b2 Var(Y) for independent X and Y - if X has a normal distribution then so does aX + b - if X and Y have independent normal distributions then aX + bY has a normal distribution - if X and Y have independent Poisson distributions then X + Y has a Poisson distribution. Proofs of these results are not required.