high School⏱ 3 min

Expected Value

Average value of random variable

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10%120%240%320%410%5E=3.00

Probabilities (any weights)

1:
10%
2:
20%
3:
40%
4:
20%
5:
10%
E[X]=∑xiP(X=xi)=3.000E[X] = \sum x_i P(X=x_i) = 3.000

Expected value = probability-weighted average of outcomes. Green line = "balance point" of the distribution. Repeat the experiment many times and the average approaches E[X].