Expected Value
The mean or average value of a random variable, calculated as E(X) = ΣxP(X = x) for discrete variables or E(X) = ∫xf(x)dx for continuous variables.
Real World
An insurance company calculates the expected payout on a car insurance policy by multiplying each possible claim amount by its probability — this expected value determines the minimum premium the company must charge to break even.
Exam Focus
Show full working for E(X) = Σx·P(X=x); do not round intermediate values as this loses accuracy marks.
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