Dr. Claudio Maccone provides a statistical equation that is called the Statistical Equation for Habitables (SEH) as well as its relationship to the Statistical Fermi Paradox. He starts by noting that the statistics of habitable planets may be based on a set of ten (and possibly more) astrobiological requirements first pointed out by Stephen H. Dole in his book “Habitable planets for man” (1964) in this one hour SETI Talk.
Dr. Maccone provides the statistical generalization of the original (too simplistic) Dole equation by replacing a product of ten positive numbers by the product of ten positive random variables. This is called the “Statistical Equation for Habitables” or SEH. His proof is based on the Central Limit Theorem (CLT) of Statistics, stating that the sum of any number of independent random variables, each of which may be arbitrarily distributed, approaches a Gaussian (i.e. normal) random variable (Lyapunov form of the CLT).
Dr. Maccone also discsses the implications of this derivation, including a practical example of how the equation can be used to find the average distance between Habitables. Finally, this result will in turn be used to discover the statistical extension of the Fermi Paradox, namely the Fermi paradox re-read in terms of probability distributions.