Is it correct that the parameters of the following distributions must be taken from the intervals given below?
Bernoulli. $p$ from $[0, 1]$
Binomial. $n$ positive integer, $p$ from $[0, 1]$
Geometric. $p$ from $(0, 1)$
Poisson. $\lambda \geq 0$
I am not sure about parameters of geometric distributions.
Could you please explain why the ranges of parameters are different? If what I wrote for geometric is true, why can't $p$ be $0$ or $1$?