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Abstract A bivariate distribution is not determined by the knowledge of the margins. Two bivariate distributions with exponential margins are analyzed and another is briefly mentioned. In the first distribution (2.1) the conditional expectation of one variable decreases to zero with increasing values of the other one. The coefficient of correlation is never positive and lies in the interval –.40≤ρ≤0, and the correlation ratio varies from –.48 to zero. In the second distribution (3.4) the conditional expectation of one variable increases or decreases with increasing values of the other variable depending on the sign of the correlation. The coefficient of correlation lies in the interval –.25≤ρ≤.25, and the correlation ratio is proportional to the coefficient.
E. J. Gumbel (Thu,) studied this question.