Howtosignalprocessing
- How do you find the correlation between two random variables?
- What is the correlation coefficient of two random variables?
- How to generate correlated random normally distributed variables?
- What is the joint distribution of two normal random variables?
How do you find the correlation between two random variables?
2 The correlation of X and Y is the number defined by ρXY = Cov(X, Y ) σXσY . The value ρXY is also called the correlation coefficient. Theorem 4.5. 3 For any random variables X and Y , Cov(X, Y ) = EXY − µXµY .
What is the correlation coefficient of two random variables?
The correlation coefficient ρXY provides a measure of how good a linear prediction of the value of one of the two random variables can be formed based on an observed value of the other.
How to generate correlated random normally distributed variables?
To generate correlated normally distributed random samples, one can first generate uncorrelated samples, and then multiply them by a matrix C such that CCT=R, where R is the desired covariance matrix. C can be created, for example, by using the Cholesky decomposition of R, or from the eigenvalues and eigenvectors of R.
What is the joint distribution of two normal random variables?
Two random variables X and Y are said to be bivariate normal, or jointly normal, if aX+bY has a normal distribution for all a,b∈R. In the above definition, if we let a=b=0, then aX+bY=0. We agree that the constant zero is a normal random variable with mean and variance 0.
