- published: 24 Jul 2012
- views: 13362
In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d.) if each random variable has the same probability distribution as the others and all are mutually independent.
The abbreviation i.i.d. is particularly common in statistics (often as iid, sometimes written IID), where observations in a sample are often assumed to be (more or less) i.i.d. for the purposes of statistical inference. The assumption (or requirement) that observations be i.i.d. tends to simplify the underlying mathematics of many statistical methods (see mathematical statistics and statistical theory). However, in practical applications of statistical modeling the assumption may or may not be realistic. The generalization of exchangeable random variables is often sufficient and more easily met.
The assumption is important in the classical form of the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution.
Run For Cover
See the man in white
He's old he wouldn't dare to fight, to fight another
Rockin' like a beast upon on a never ending dream
We love each other
Asking for a sign- the action's coming from behind
Let's run for cover
Feel the music's beat, we fight for rock
And in the heat we stand together
We're holding back for you when you fight
And we stand for one another
We're holding back for you, when you run for cover
And see those open eyes
When you are standing here tonight
That's why- We're holding back for you, when you run for cover
Restless in the night, we all stand up for this delight
We fight together
We're holding back for you when you fight
And we stand for one another
We're holding back for you, when you run for cover
We're holding back for you.......