Law of the unconscious statistician

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In probability theory and statistics, the law of the unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability distribution of X. The form of the law depends on the type of random variable X in question. If the distribution of X is discrete and one knows its probability mass function pX, then the expected value of g(X) is E ⁡ [ g ( X ) ] = ∑ x g ( x ) p X ( x ) , {\displaystyle \operatorname {E} [g(X)]=\sum _{x}g(x)p_{X}(x),\,} where the sum is over all possible values x of X. If instead the distribution of X is continuous with probability density function fX, then the expected value of...

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