### The Black Swan reloaded

In The Black Swan Nassim N. Thaleb suggests extreme uncertainty, the Black Swans, explain almost everything about our world. Unfortunately the book is vague and full of endless passages going nowhere. Here I give you a concise version from my point of view. Exponential distributions: Thaleb’s white swans You want to know how fast COVID-19 passes along a chain of n +1 individuals. You learn about the generation time interval, the time it takes from the infection of one individual to the next. You’re told the generation time interval is a random variable with a gamma distribution with shape parameter a and scale parameter T , which is quite realistic. The time it takes COVID-19 to pass along the chain of n +1 individuals is the sum of the n generation time intervals associated with each of the n transmission events: S n = T 1 + T 2 +...+ T n . Now you remember the central limit theorem (Feller 1971, ): when n is large the distribution of S n can be approximated by a Normal dist