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I would be really happy to recieve some help. I have tried using Jacobians and so on, but

I am stuck.

I'll start with the univariate case. Let X ~ N(μ,σ) and Y = exp(X)/(1+exp(X)). What is the joint f(x,y)? According to intuition fy|x = 1, but since we are dealing with continous distributions I am not sure.

The bivariate case is an extension. Let X1, X2 be bivariate normal and

Y = exp(γ1*X1 + γ2*X2)/(1 + exp(γ1*X1 + γ2*X2) ), where the gammas are just

constants. Now I am looking for f(x1,x2,y). Any suggestions of how to proceed at least?

/H

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# Joint of normal and logistic

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