Contents
What is covariance for independent random variables?
Covariance can be positive, zero, or negative. If X and Y are independent variables, then their covariance is 0: Cov(X, Y ) = E(XY ) − µXµY = E(X)E(Y ) − µXµY = 0 The converse, however, is not always true. Cov(X, Y ) can be 0 for variables that are not inde- pendent.
When independent variables are highly correlated, change in one variable would cause change to another and so the model results fluctuate significantly. The model results will be unstable and vary a lot given a small change in the data or model.
What is cov X Y?
The covariance, denoted with cov(X;Y), is a measure of the association between Xand Y. De nition: cov(X;Y) = E(X . X)(Y . Y ) This can be simpli ed as follows: cov(X;Y) = E(X . X)(Y . Y ) = E(XY) . Y E(X) .
What is the variance of two random variables?
The variance of the sum or difference of two independent random variables is the sum of the variances of the independent random variables. Similarly, the variance of the sum or difference of a set of independent random variables is simply the sum of the variances of the independent random variables in the set.
What is the difference between variance and correlation?
The difference between variance, covariance, and correlation is: Variance is a measure of variability from the mean Covariance is a measure of relationship between the variability (the variance) of 2 variables. Correlation/Correlation coefficient is a measure of relationship between the variability (the variance) of 2 variables.
What are the properties of variance?
Basic Properties of the Variance. One useful result about variances which is relatively easy to show is that because the variance gives a measure or the square of the width of a distribution, the variance of a constant times a random variable is the square of the constant times the variance of the random variable.