The expectation value of a function f(x) in a variable x is denoted 〈f(x)〉 or E{f(x)}. For a single discrete variable, it is defined by 〈f(x)〉 = sum_x f(x) P(x), where P(x) is the probability density function. For a single continuous variable it is defined by, 〈f(x)〉 = integral f(x) P(x) d x. The expectation value satisfies 〈a x + b y〉 | = | a〈x〉 + b〈y〉 〈a〉 | = | a 〈 sum x〉 | = | sum〈x〉.
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