I cannot understand the identically distributed part in the i.i.d assumption. Consider a site percolation where each event is a Bernoulli variable. Does this mean that each event is independent of each other? Do I need to check some conditions to make sure this assumption is valid?
I am interested in two-terminal reliabily that is the probability that two terminals are connected by some path.
Example.
When I calculate the reliability over the Bernoulli variables, does the inclusion-exclusion formula becomes just a $\pm$sum without intersection terms?
Is a site percolation with Bernoulli variables i.i.d. or what does it mean to be identically distributed?