Ned Batchelder writes: > Thomas: let's say I generate streams of N digits drawn randomly from > 0-9. I then consider the probability of a zero *never appearing once* > in my stream. Let's call that P(N). Do you agree that as N > increases, P(N) decreases?
In probability theory, that could be phrased as the probability that N unknown digits d_1, ..., d_N are all positive, assuming the digits are independent (so learning one digit doesn't reveal anything about any other digit), and for each d_k, the probability p_k of having a positive digit is the same. Mathematicians often abbreviate these assumptions as "i.i.d" for "independent" and "identically distributed". Also assuming uniform distributions, p_1 = p_2 = ... = p_N = 9/10. P(d_k > 0 for k = 1, ..., N) = P(d_1 > 0 and d_2 > 0 and ... and d_N > 0) = (by independence) P(d_1 > 0) * P(d_2 > 0) * ... * P(d_N > 0) = p_1 * p_2 * ... * p_N = (by identical uniform distribution) (9/10)^N In mathematics, (9/10)^N decreases as N increases, so one should indeed agree. Using more impressive notation and terminology correctly will not change the analysis. -- https://mail.python.org/mailman/listinfo/python-list
