How would you go about explaining i.i.d (independent and identically distributed) to non-technical people?
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It means "Independent and identically distributed".
A good example is a succession of throws of a fair coin: The coin has no memory, so all the trows are "independent".
And every throw is 50:50 (heads:tails), so the coin is and stays fair - the distribution from which every throw is drawn, so to speak, is and stays the same: "identically distributed".
A good starting point would be the Wikipedia page.
Independence is a very general notion. Two events are said to be independent if the occurrence of one does not give you any information as to whether the other event occurred or not. In particular, the probability that we ascribe to the second event is not affected by the knowledge that the first event has occurred.
If a random variable $X$ comes from a population having (say) a normal distribution, that is its pdf (probability density function) is that of normal distribution, with a population average $\mu=3$ and population variance $\sigma^2=4$ (the numbers are hypothetical and are just for your understanding and to simplify comparisons) we can describe it as follows: $X \sim N(3 , 4)$.
Now if we have another random variable $Y$ which is also normally distributed and which is $Y \sim N(3, 4)$ then $X$ and $Y$ are identically distributed.
Nevertheless, being identically distributed does not necessarily imply independence.