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If I want to measure an empirical average of the sum of coin tosses (heads = 0, tails = 1) after 10 tosses and and after 100 tosses and I want my average to be based off of 1000 trials, is it "ok" to reuse the experiments of after 10 tosses for the after 100 tosses?

What I mean is for the first average I will toss a coin 10 times get the sum, and do this 1000 times and get an average for the sum.

So I will have tossed a coin 10 * 1000 times. I store a 1000 by 10 array where each row contains the 10 tosses of the corresponding experiment.

Now I want to calculate the average sum of coin tosses after 100 tosses. Instead of tossing a coin 100 * 1000 times can I reuse the 10 * 1000 tosses from my previous experiment and then only toss a coin 90 * 1000 times? Or are there problems with this?

I realize that my measurements of the average for 10 tosses and 100 tosses will be dependent, but does that mean they are wrong? As in a wrong calculation of the empirical average?

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    $\begingroup$ The "empirical average" is not estimated: it's a number that is calculated from the data. The calculation is either correct or not. Are you sure "empirical average" is the term you mean to be using? $\endgroup$
    – whuber
    Aug 15, 2017 at 17:23
  • $\begingroup$ sorry I will update it. I do not mean estimating the empirical average. I mean measuring the empirical average and using it as an estimate of the true mean. $\endgroup$ Aug 15, 2017 at 17:29

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As a coin toss can be considered independent of previous number of tosses (i.e. memoryless) then there shouldn’t be any issue with this.

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I hope you are not tossing the coin physically (joke) =)
For your question, if you toss one coin and toss the same coin after (which does not depend on the previous outcome), they are independent. Whether you do it 10 times or 100 times, you have 10 or 100 independent tosses. So if you were to use to find an empirical mean for each, it's not a problem.

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  • $\begingroup$ yes, this is what I figured except I was thinking that if I was reporting my results on the average of some parameter and then reused some data for a different measurement then these two measurements are correlated and therefore there is an increased probability that they are both biased. Anyways, thanks for the answer. $\endgroup$ Aug 15, 2017 at 16:38

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