Black Swans
https://arxiv.org/pdf/2104.07693.pdf @astronomy @david-kipping @probability
I thought this was an interesting concept, and from David’s video, it reminded me of the position of Ellie at the end of @contact.
One of the questions that David is trying to answer is, if you take something like the ‘wow’ signal, how might we determine if it will happen again? How do we determine if it’s a once off event or at least assign some reasonable certainty that it’s a once off event.
The attempt is to put a number on the rate of occurrence of the unprecedented event in time.
Poisson Distribution
https://www.youtube.com/watch?v=jmqZG6roVqU
A Poisson random variable (X) is a count of the no. of occurrences of an event (in some time, volume etc.)
- Events must be independent.
- The rate of occurrence does not change (through time or volume or whatever).
If these events hold then the random variable X has the Poisson distribution.
Probability the random variable X, takes on the value x is:
The mean and the variance are equal. is the mean number of occurences.
In PDF’s (Probability Densitry Functions) ranges are the defautl, in a discrete setting, a range of outcomes is some summation.