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Calculate the expected value (mean) of a discrete random variable from its probability distribution.
Each outcome 1-6 has P = 1/6
E(X) = (1+2+3+4+5+6)/6 = 3.5
Win $100 with P=0.01, lose $2 otherwise
E(X) = 100(0.01) - 2(0.99) = -$0.98
Expected value is the long-run average outcome if you repeated the experiment many times. It's not necessarily an outcome that can actually occur (like 3.5 for a die roll).
Expected value helps compare options. A positive expected value means you'll gain on average; negative means you'll lose. It's used in gambling, insurance, investments, and business decisions.