Linear Combination
For independent random variables X and Y with E(X)=μₓ, Var(X)=σₓ², E(Y)=μᵧ, Var(Y)=σᵧ², the linear combination Z = aX + bY has E(Z) = aμₓ + bμᵧ and Var(Z) = a²σₓ² + b²σᵧ² (if X and Y are independent).
Real World
A delivery company like DPD estimates total route time by adding individual leg times: if each leg has its own mean and variance, the overall journey variance uses the linear combination rule to plan realistic delivery windows.
Exam Focus
Remember: variances add only when variables are independent — state this assumption explicitly for full marks.
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