Bayesian Statistics for Beginners: a step-by-step approach

The left side of the equation can be read, “What is the probability that a random variable called X has a value of x, given λ.”

The Poisson pmf has just one parameter that controls both its shape and location. This parameter is called “lambda” and is written λ. It represents the mean number

possible values that x can assume for the Poisson distribution (x ¼ 0; 1;:::) is not finite; rather it is “countably infinite.”

Poisson probability mass function is written: PrðX ¼ x; λÞ ¼ λx e−λ x! x ¼ 0; 1; 2;::: ð11:1Þ where λ is the mean number of occurrences in a given period of time, x is the number of occurrences we are interested in, and e is the natural logarithm constant (approximately 2.718),

“There is something in probability theory called a Poisson process, giving amazingly good descriptions of such random independent events occurring through time, like customer arrivals at a fast-food store, cosmic rays striking a planet, accidents in a factory, airplane mishaps, and maybe shark attacks.”