Generate correlated random variables

1. How do you generate correlated random variables?
2. How do you correlate two random variables?
3. How do I generate correlated data in Excel?
4. Can independent random variables be correlated?

How do you generate correlated random 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.

How do you correlate 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 .

How do I generate correlated data in Excel?

The Excel Correlation Formula

Calculate the sum of variable X minus the mean of X. Calculate the sum of variable Y minus the mean of Y. Multiply those two results and set that number aside (this is the first result). Square the sum of X minus the mean of X.

Can independent random variables be correlated?

So, yes, samples from two independent variables can seem to be correlated, by chance.