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If I have a bag filled with numbered balls. The numbers are from say 1 to 10. But the number of balls follow poisson distribution with lambda=1.

Just a graph like below enter image description here

Now I want to make sample of 30 using random sampling. If I draw a sample of 30 balls without replacement should it be called as random sampling ?

Because as far as I understood random sampling It is a process of choosing observations in which each observation from population has equal probability of get picked to be in sample.

But if I choose any balls from the bag in my above example the probability of balls numbered 0 and 1 getting picked will be higher than probability of balls numbered 7 and 8.

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If you draw a sample equally favoring each ball in the bag - disregarding the number on the ball - it will be a random sample.

If the expectation is that you want the random sample to have a similar distribution as the balls in the bag, then sampling with replacement is better.

But, if the number of draws is small (and the bag is big), the weather you replace them or not should not matter much.

See here and here on corrections when sampling without replacement.

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  • $\begingroup$ Yes the balls are drawn equally favouring each ball. No bias to any numbered ball. So then it should be a random sample. Right ? If yes then the sample should contain more small numbered balls than large numbered balls, right ? $\endgroup$ Jun 27, 2020 at 8:47
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    $\begingroup$ Yes, for the case in the question (that is a small sample is drawn randomly without replacement from a bag with a large number of balls) $\endgroup$ Jun 28, 2020 at 1:44

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