# 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).

• i.i.d. is short for "identical and independently distributed". It means that all the random variables in your sequence have the same probability distribution and are independent of each other. – suresh May 8 '14 at 23:44

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.

• What does this mean? "where the probability of a channel being occupied by any primary user in any slot is assumed to be i.i.d" (line 4 in the figure above). – x.y.z... May 9 '14 at 15:31

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 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!