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The Poisson distribution can be interpreted as a propability distribution that returns how likely it is that a certain number of events will occur, when the mean is known. Regardless it's formula, whats the the intuition behind the shape of that distribution? Why is it not symmetrical around the mean? example from wikipedia

Pluxyy
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    Symmetrical? How would you define the probability of a negative number of occurrences? – Jean-Claude Arbaut Jan 12 '21 at 13:00
  • The previous comment gets at the basic principle here. Pretend the mean is 1 event in a unit of time, T. Then you can only have 0 events to the left of the mean, but to the right of the mean, you can have an infinite amount. I don't think it would make sense to say P(X=0) = P(x=1) = P(X=2) = 1/3 and then assume could never be greater than 2. The poission attempts to model the count of events whose time between events is memoryless (i.e. exponential). So, by this definition alone we need to account for X >= 3 with a significant amount of mass in the distribution. Hence the skewness. – wjamdanf1234 Jan 12 '21 at 13:12
  • Note that by the CLT, symmetry around the mean is 'recovered in the limit' also for the Poisson distribution. In other words, the Poisson distribution asymptotically recovers its symmetry around its mean as the $\lambda$- or time-parameter is sent to infinity. – 5th decile Jan 12 '21 at 13:20

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