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I would like to mention that I don't have a mathematical background but I am taking probability modelling and statistical inference course in a University for my business analytics degree. I would like to express my conceptual doubt over what we exactly mean by IID:

My interpretation:

For example in rolling a dice 17 times (1 sample of size 17):

1st sample: Set A (#Rolls: 1-17): 1, 6, 3, 2, 5, 4, 2, 1, 6, 5......17 times
2nd sample: Set B (#Rolls: 18-34): 6, 1, 4, 3, 2, 5, 3, 1,......17 times

Here, every observation (like 1, 6, 3 and so on...) in Set A (which is a sequence) is an IID. It means that: my Set A had 17 random variables like 17 blanks before sampling started and each of those 17 blanks (or random variable ) before filling with observations could had taken any value between 1 & 6 and hence identically distributed. And each of those 17 blank's outcome is independent of previous blanks' outcomes Combining last 2 points my every observation can be called IID.....

Am I understanding it correctly?

  1. My doubt is: Do we call the samples (like sample 1, sample 2 and so on) as IID or the observations in 1 single sample as IID ?

Any corrections are very most welcome. I wanted to tag the question as IID but I cant do with my reputation. I had asked my professor with the same text this weekend but could not understand her reply in the context of my doubt:

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1. Y1, Y2, Y3 i.i.d. refer to three random variables are independent with identical distribution.
2. An observation is a realized value from an originally random variable under certain probability distribution

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IID is the abbreviation for "independent and identically distributed". It applies to random variables.

In this example, each of the $34$ die-rolls is a random variable. They are independent because they don't influence each other: when you roll a die it (ideally) has no memory of the results of previous rolls. They are identically distributed because they all have the same distribution: probability $1/6$ for each of the $6$ possible outcomes $1,2,3,4,5,6$.

When you do the experiment, you get an outcome: the observations $ 1, 6, 3, 2, \ldots$. These are not random variables (and thus can't be called IID), they are observations of a random variable (or a sample from the distribution of the random variable).

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  • $\begingroup$ Thank you, Professor @Robert. Your explanation helps me in understanding the nuances of this concept. I hope you won't mind me asking more questions as I learn. Have a nice day. $\endgroup$ Nov 20, 2017 at 19:33

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