Expectation Algebra
Mathematical rules for expected values: E(aX+b) = aE(X)+b, E(X+Y) = E(X)+E(Y), and E(XY) = E(X)E(Y) when X and Y are independent.
Real World
An actuary at Aviva Insurance applies E(aX + b) to calculate the expected total payout when each claim X is scaled by a policy multiplier and a fixed administration fee is added.
Exam Focus
Show each algebraic step when simplifying E(aX + b) — collapsing too quickly loses working marks even if the answer is correct.
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