Assertion: variable's variance | /r/HasProperty | equal
Facets:
value: to their average correlation
type: OTHER
value: to the sum of their variances
type: OTHER
value: approximately
type: DEGREE
value: in other words
type: DEGREE
Source sentences:
text: In other words, the variance of X is equal to the mean of the square of X minus the square of the mean of X.
text: It follows immediately from the expression given earlier that if the random variables X 1 , … , X N {\displaystyle X_{1},\dots ,X_{N}} are uncorrelated, then the variance of their sum is equal to the sum of their variances, or, expressed symbolically:
text: The formula states that the variance of a sum is equal to the sum of all elements in the covariance matrix of the components.
text: Therefore, the variance of the mean of a large number of standardized variables is approximately equal to their average correlation.