It means "Independent and identically distributed".

You are watching: If x and y are independent and identically distributed with mean

A good example is a sequence of throws of a fair coin: The coin has actually no memory, so every the throws are "independent".

And every throw is 50:50 (heads:tails), so the coin is and stays same - the distribution from i m sorry every throw is drawn, so come speak, is and stays the same: "identically distributed".

A great starting allude would be the Wikipedia page.

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Follow this link to further check out the concept.

$egingroup$ So, is it not essential that the IID arbitrarily variables need to be equi-probable? if they are not equiprobable then how have the right to the "identically distributed" it is in explained? thanks a many in advance... $endgroup$

Nontechnical explanation:

*Independence* is a very general notion. Two occasions are claimed to it is in independent if the incident of one go not give you any kind of information as to whether the other event developed or not. In particular,the probability that us ascribe come the 2nd event is not affectedby the expertise that the very first event has actually occurred.

**Example of live independence events, perhaps identically distributed**Consider tossing two various coins one after the other. Presume thatyour ignorance did not acquire unduly tired when the flipped the first coin,it is reasonable to i think that understanding that the first coin toss caused Heads in no means influences what girlfriend think the probabilityof heads on the 2nd toss is. The two occasions $$\textfirst coin toss led to Heads~~ extand~~\textsecond coin toss led to Heads$$are claimed to be *independent* events.

If us know, or obstinately insist, the the 2 coins have actually differentprobabilities of leading to Heads, then the occasions are *notidentically distributed.See more: Final Fantasy 15 Stealing The Past Sidequest Guide, Stealing The Past Sidequest Guide*

If us *know* or *assume*that the 2 coins have actually the *same* probability $p$ that comingup Heads, climate the above events are also *identically distributed,*meaning that they both have actually the exact same probability $p$ of occurring.But an alert that uneven $p = frac 12$, the probability of Headsdoes not equal the probability of Tails. As detailed in one of theComments, "identical distribution" is not the same as "equallyprobable."

**Example the identically spread nonindependent events**Consider one urn with two balls in it, one black and also one white.We reach right into it and draw out the 2 balls one after the other,choosing the first one at random (and this of course determinesthe color of the following ball). Thus, the 2 equallylikely outcomes of the experimentare (White, Black) and (Black, White), and we view that the firstball is equally most likely to be black color or White and also so is the secondball likewise equally likely to be black or White. In various other words,the events$$\textfirst ball drawn is Black~~ extand~~\textsecond ball drawn is Black$$certainly space identically distributed, but they are definitely**not** independent events. Indeed, if we know that the firstevent has occurred, we recognize for certain that the second *cannot*occur. Thus, while our initial testimonial of the probabilityof the 2nd event is $frac 12$, as soon as we recognize that the firstevent has occurred, we had finest revise our assessment of theprobability of the 2nd drawn will certainly be black color from $frac 12$ come $0$.