So almost everywhere in the book it's written "random variables are IID", what does this mean?
I think it means independent and identically distributed but not sure.
So by definition A and B R.V are independent means that:
$p(A\cup B)=p(A)+p(B)$ right?
But what does identically distributed mean? Does it mean that the variables have the exact same distribution?
Thanks a lot!
$\endgroup$ 42 Answers
$\begingroup$It means independent and identically distributed. You are correct.
$\endgroup$ $\begingroup$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!
$\endgroup$
