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?