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I am confused with the concept of completely random actions. I was thinking of a very common statistical experiment in which we have a device or black box which randomly chooses between 1 and -1. If we infinitely do this processes, we will have set of randomly chosen infinite 1's and -1's. If we sum up all the elements of this randomly generated set we will probably get 0 every time we perform this experiment. This implies that it is a biased random as it is following the constraint that sum of elements of randomly generated infinite set is 0 every time.

But I was wondering, since the above procedure of choosing between 1 and -1 is completely random, then the sum of all the elements of randomly generated set must be a random number instead of being zero every time. If the sum of elements is any random number, then only it must be called as a unbiased random number and hence confirming the performed experiment to be random.

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  • $\begingroup$ You might find it worth asking this question on Phil.SE rather than physics as it looks likely that you're confused conceptually about what constitutes randomness; simply because a sequence is random does not mean that there are not determined quantities about it; as you've already pointed out, the mean or average is a determined number; another, very simple fact, is that we only see 0 and 1s, but that of course is tautological. $\endgroup$ – Mozibur Ullah Dec 15 '17 at 21:31
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    $\begingroup$ I'm voting to close this question as off-topic because it is about mathematics not physics. $\endgroup$ – sammy gerbil Dec 15 '17 at 21:53
  • $\begingroup$ The conceptual confusion arises because we're using determinate in at least two different ways here. $\endgroup$ – Mozibur Ullah Dec 15 '17 at 22:01
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That's why it's preferable to be precise and say that these numbers are not simply "random numbers", but rather random variables that follow a probability distribution, which, in the black box example, is the sum of two Dirac delta functions centered on $-1$ and on $+1$.

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