Expected Values and Fair Games

For a discrete random variable, E(X)= _x xP(X=x). This is a probability-weighted long-run average; it need not be a possible outcome. **Value x** | **0** | **2** | **5** P(X=x) | 0.5 | 0.3 | 0.2 For this prize distribution, E(X)=0(0.5)+2(0.3)+5(0.2)=1.6. A fair entry fee is 1.6 units of money: expected net gain is zero. Distinguish a gross prize from net gain after paying the fee. If an event has probability p on each of n trials, its expected number of occurrences is np. For 80 deliveries each with delay probability 0.03, the expected number delayed is 2.4; this is not a claim that a realised count can be fractional.