The variance of is often denoted by , , or simply . The exponent on is put there so that the number is measured in the same units as the random variable itself.
The quantity is called the standard deviation of ; because of the compatibility of the measuring units, standard deviation is usually the quantity that is quoted to describe an emprical probability distribution, rather than the variance.
The variance is a measure of the dispersion or variation of a random variable about its mean .
It is not always the best measure of dispersion for all random variables, but compared to other measures, such as the absolute mean deviation, , the variance is the most tractable analytically.
The variance is closely related to the norm for random variables over a probability space.
The variance of is the second moment of minus the square of the first moment:
This formula is often used to calculate variance analytically.
A random variable is constant almost surely if and only if .
The variance can also be characterized as the minimum of expected squared deviation of a random variable from any point:
|Date of creation||2013-03-22 11:53:46|
|Last modified on||2013-03-22 11:53:46|
|Last modified by||stevecheng (10074)|