The expected value of a variable is the long-run average value of
that variable. The expected value of a statistic is therefore the
mean of the sampling distribution
If the expected value of a statistic is the
the statistic is an unbiased
Expected values of variables are indicated by an "E" with the
variable enclosed in brackets. Thus, E[X] is read as the expected
value of X.
Some basic rules of expected values are shown below:
- E[X] = μ where μ is the mean of
- σ² = E[X - μ]² where σ² is the variance of
X and μ is the mean of X.
- E[X]² = σ² + μ²
- E[X + Y] = E[X] + E[Y]
- E[XY] = E[X]E[Y] if X and Y are independent.
- In general, E[X/Y] does not equal E[X]/E[Y]