Contents
What is the total variance of a matrix?
For instance, in a 10 x 10 matrix, the trace is the sum of the diagonal elements. The total variation, therefore, of a random vector is simply the trace of the population variance-covariance matrix. Thus, the total variation is equal to the sum of the population variances.
Can variance be a matrix?
Variance and covariance are often displayed together in a variance-covariance matrix, (aka, a covariance matrix). The variances appear along the diagonal and covariances appear in the off-diagonal elements, as shown below.
How do I find the VAR of aX?
Var(aX + bY) = a2 Var(X) + b2 Var(Y) + 2abCov(X,Y). = a2 Var(X) + 2abCov(X,Y) + b2 Var(Y). Var(aX + bY) = a2 Var(X) + b2 Var(Y).
What is the variance of a matrix?
A variance-covariance matrix is a square matrix that contains the variances and covariances associated with several variables. The diagonal elements of the matrix contain the variances of the variables and the off-diagonal elements contain the covariances between all possible pairs of variables.
What is the variance between X and Y?
In the following table, the variances are displayed in bold along the diagonal; the variance of X, Y, and Z are 2.0, 3.4, and 0.82 respectively. The covariance between X and Y is -0.86. The variance-covariance matrix is symmetric because the covariance between X and Y is the same as the covariance between Y and X.
How is the variance-covariance matrix symmetric in ith?
The variance-covariance matrix is symmetric because the covariance between X and Y is the same as the covariance between Y and X. Therefore, the covariance for each pair of variables is displayed twice in the matrix: the covariance between the ith and jth variables is displayed at positions (i, j) and (j, i).
Where do you find the covariances in a matrix?
The diagonal elements of the matrix contain the variances of the variables and the off-diagonal elements contain the covariances between all possible pairs of variables. For example, you create a variance-covariance matrix for three variables X, Y, and Z.