Definition:Variance/Continuous
< Definition:Variance(Redirected from Definition:Variance of Continuous Random Variable)
Jump to navigation
Jump to search
Definition
Let $X$ be a continuous random variable.
Then the variance of $X$, written $\var X$, is a measure of how much the values of $X$ varies from the expectation $\expect X$, and is defined as:
- $\var X := \expect {\paren {X - \expect X}^2}$
That is, the expectation of the squares of the deviations from the expectation.
Letting $\mu = \expect X$, this is often given as:
- $\var X = \expect {\paren {X - \mu}^2}$
Also denoted as
In contexts where the standard deviation is of interest, the variance is often denoted ${\sigma^2}_X$.