I am currently trying to derive the joint probability density function for two random dependent variables each with a marginal distribution following an F22 distribution. Is there a way to derive the joint pdf for two dependent variables knowing their marginal distribution, even if its just in terms of their correlation?

I am also looking to derive the probability density function of their sum. As they are dependent the sum formula can not be used. Is there a way to find the distribution of the sum of two depedent variables knowing their marginal distribution?

Thanks so much for your help!!!