# Thread: Covariance and Expected Value?

1. ## Covariance and Expected Value?

Hello
I just read the following two equations and I need some help in understanding them.

1. cov {ηr(x, t), ηr(u, τ)} = Cηr (x − u)δ(t − τ)

The first one might be a covariance of the two function nr(x,t) and nr(u,τ). I do not get the C (big c) on the right side of the equation.

2. E{νr(x, t)sr(u, t)} = E{ηr(x, t)sr(u, t − 1)} = 0

The number two must refer to the Expected value or mean value . So I think that the author want to express the expected value for two variables. If that is correct then why there is no comma between vr(x,t) and sr(u,t).

What might be the meaning of this equation? Two different equations that equal zero.

Best Regards
Alex

2. can you post more from the book/paper?
I have no idea what kinds of functions these are.
The first one is a covariance and the second is an expectation.
In the second one there is a shift going on, which is dependent on these functions,
causing there to be a zero correlation.

3. Originally Posted by dervast

1. cov {ηr(x, t), ηr(u, τ)} = Cηr (x − u)δ(t − τ)

2. E{νr(x, t)sr(u, t)} = E{ηr(x, t)sr(u, t − 1)} = 0

nr(x,t) and nr(u,t) are spatially colored yet temporally white zero-mean Guassian stationary random fields with separable covariance structure.