# Is there any need of random sampling for IID Data?

I understand that random sampling is required for the purpose of creating an unbiased sample with the same characteristics as the population. I am confused about whether random sampling is required for IID data. Consider the following thought experiment. I toss a fair die a million times. Each time I toss the die, I note the number that appears on the die on a piece of paper and put the paper into a bowl. The numbers in the pieces of paper in the bowl are now realizations of IID random variables. The tosses are independent and each time the outcome is one of the numbers 1 to 6 with probability of 1/6. Now suppose I DO NOT shuffle the pieces of paper in the bowl and conveniently pick 10 pieces of paper from the top of the bowl. Isn't my sample an IID sample ? Is there any need to shuffle the pieces of paper in the bowl given the fact that I know that the random process that generated the population data is stationary and therefore any sample that I draw from the population is a realization of IID random variables ?

• You have essentially added an additional layer of randomness, and then said that it's not random. But the dice rolls were random, and then you shuffled them, and they are still random. If you remove the shuffling stage, they don't stop being random. Commented Dec 22, 2020 at 5:07
• Thanks for your answer. What about my original question ? Is there any need to randomize the sampling process for data that has been generated by a stationary process ? Commented Dec 22, 2020 at 5:12