Suppose that you have a probability distribution P of a parameter which, for simplicity, it is two-valued. For example, it could be a coin where we denote heads with "+" and tails with "-". Suppose that we throw the coin N times, and the results tend to follow the probability ditribution P for large enough N (which naturally could be 50%-50%). We then calculate the mean value of all these results, which are a series of "+" and "-" (N in total), and find a number <S>. Suppose now, that, we erase M of these results (with M<N) from the total N, and we are left with the rest N-M results. BUT, we do the erasure with a completely random way. We calculate, again, the mean value with the N-M results, <S'>. QUESTION Will the mean values <S> and <S'> be equal? The answer will surely depend on the numbers N, M. Is there any known theorem about this, that guarantees the equality for appropriate N, M? Edit: For finite N, M ofcourse the equality is impossible. What i mean is whether <S'> can approach <S> very very close, for appropriate N, M.