Expected value

E(X)=\sum x_i p_i

Result unit: — (liczba)

What it describes

The average value of a random variable weighted by probabilities.

E(X)

expected value

x_i

values of the variable

p_i

probabilities

This is the "average result in the long run" — we weight each value by its probability. It need not be one of the possible outcomes.

Games of chance, risk, assessing whether a bet is worthwhile.

A prize of 10 zł with probability 0.3, and 0 zł with probability 0.7. Find the expected value.

Substitution

10\cdot0.3+0\cdot0.7

Result

E(X)=3

zł.

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