What does a probability being i.i.d means? I know that a sequence of random variables is i.i.d means that they have the same mutually independent probability distribution.
I was reading in a paper where the authors said that "the probability of an event A is assumed i.i.d".
What does it mean that a probability is i.i.d? Does this make any sense?
Thanks.
EDIT: Here is the article.
And here is a snapshot (in case someone cannot have access).

 A: No, it doesn't make sense to speak of a single event, or the probability of a single event, as being iid.  However, if you post more context (or a reference to the paper itself), it may become more clear what the authors meant.
A: i.i.d. stands for independent, identically distributed. It means the random variables are independent and have the same distributions. However, it does not make sense to refer to an event as i.i.d.
A: a probability being i.i.d (independent and identically distributed) can basically be expressed in two steps: 
1) when the outcomes of a random variable does not affect each other "independent".
2) when the outcomes share the same distribution with the same parameters. For example, assume the distribution to be N(0,1/2), that is normal with mean=0 and variance=1.
I will give you a concrete example of (i.i.d.), think of tossing a coin 'n' number of times. Now, in this case, our random variable is "coin", the probability of having head is =1/2 and the probability of having no head is = 1/2. Therefore, they are "identically distributed"! Also, the outcomes are "independent", they do not affect each other! Therefore, this probability is (i.i.d.)!
I hope this makes it clear and easy!
