In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.Informally, it measures how far a set of (random) numbers are spread out from their average value.
Variance describes the degree of dispersion of a random variable.
definition:
The variance of a random variable X is:
This definition covers random variables that are continuous, discrete, or both. The variance can also be used as the covariance of a random variable with itself:
For continuous random variables:
f(x) is the probability density function of XFor discrete random variables:
nature
1. A constant random variable has a variance of 0
2. Translation does not change the variance of the random variable
3. Scaling changes the variance by a factor of square 4. The variance Cov(X,Y)
of the sum of two random variables represents the covariance of X,Y
variance
