Howtosignalprocessing
- What properties of a random process make it a Gaussian process?
- How do you prove a random process is Gaussian?
- Are Gaussian random variables independent?
- What does sigma refers to in Gaussian random variable?
What properties of a random process make it a Gaussian process?
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed.
How do you prove a random process is Gaussian?
A random process X(t) is Gaussian if its samples X(t1),..., X(tn) are jointly Gaussian for any n ∈ N and distinct sample locations t1, t2,..., tn. Gaussian random process. output is also a Gaussian random process. Sn(f) = N0 2 .
Are Gaussian random variables independent?
They are not independent. You may find this helpful from a practical standpoint. stats.stackexchange.com/questions/15011/… In addition to the nice examples given consider generally a bivariate normal distribution with N(0,!)
What does sigma refers to in Gaussian random variable?
The PDF of a Gaussian random variable, z, is given by. where μ is the mean of the average value of z and σ is its standard deviation.
