Uncorrelated random process

1. What is uncorrelated random variable?
2. Are uncorrelated processes independent?
3. How do you know if two random variables are uncorrelated?
4. How do you know if something is uncorrelated?

What is uncorrelated random variable?

In probability theory and statistics, two real-valued random variables, , , are said to be uncorrelated if their covariance, , is zero. If two variables are uncorrelated, there is no linear relationship between them.

Are uncorrelated processes independent?

Uncorrelation means that there is no linear dependence between the two random variables, while independence means that no types of dependence exist between the two random variables. For example, in the figure below and are uncorrelated (no linear relationship) but not independent.

How do you know if two random variables are uncorrelated?

Correlation measures linearity between X and Y. If ρ(X,Y) = 0 we say that X and Y are “uncorrelated.” If two variables are independent, then their correlation will be 0.

How do you know if something is uncorrelated?

We say that X and Y are uncorrelated if ρ(X, Y ) = 0; equivalently, if Cov(X, Y ) = 0. A significant property of uncorrelated random variables is that Var(X + Y ) = Var(X) + Var(Y ); see Theorem 15.4(2).