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This is the logistic distribution of single random variable (taken from Wikipedia).

x = random variable mu = mean of all random variables s = variance.

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Now, I want to do a Bivariate logistic distribution (having two random variables x1 and x2). My dataset is going to be image pixel values!

When I find the covariance of two random variables, it turns out to be a 2 x 2 square matrix but I need a single number! How to actually compute a bivariate model?

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The covariance of any multivariate distribution is always a matrix. Maybe it is of help to you to know what this matrix contains:

-In general, each entry i,j of the matrix gives you the correlation between the RVs i and j.

-So a diagonal element i,i will simply be the variance of the RV i.

-If RV i and j are independent, then the non-diagonal entry i,j is zero (they are uncorrelated). The reverse of this statement is not generally true, but it is for Gaussians iirc.

I don't know what you are trying to do, but perhaps the trace of the matrix or its determinant is of use to you?

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