Real random variable

Expectation

The expectation of a Real random variable may be thought of as the value which the variable is most likely to be close to. It has different but similar definitions for a Discrete variable and a Continuous variable.

Discrete variable

For a Discrete random variable the expected value is defined as follows

Expectation value may also be found by summing the Survival function

Proof

proof

Continuous variable

For a continuous random variable Continuous random variable the expected value is defined as follows

Properties

The expected value has the following useful properties, where and are random variables (possibly dependent) and are constants.

3. for independently distributed

Proof of 3

Since

as required by ^P3.

See also

• Law of the unconscious statistician

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