on a random string of digits number 123 appears every 1000 digits, 221 every995digits

[WTE_Galway]

Originally Posted by salmo

There are problems with your methodology. The datatset you are using (1 Million Digits of Pi) is NOT random for your purposes. May I suggest you download a randomly generated dataset from somewhere like www.random.org or find other sources of random data and re-run your analysis. I assure you, that p(1,2,3) = p(2,2,1) = 1/1000

Actually you are both wrong.

For example, given a set of real numbers {1,2,3 ... 10000}

The string 123 occurs 11 times {123, 1123, 1230, 2123, 3123, 4123, 5123, 6123, 7123, 8123, 9123} as does the string 223 {223, 1223, 2223, 2230, 3223, 4223, 5223, 6223, 7223, 8223, 9223}.

Thus the probability is 1:1000 for 1000 real numbers but 11:10,000 for 10,000 real numbers.

The probability changes with sample size, getting larger as the set of reals being sampled gets larger.

You need to work out probabilities for a population rather than a sample.

You can of course manipulate the sample size to get aberrant results. For example the set of reals {1,2,3 ... 1200} has two elements containing the string 123 and only one element containing the string 223. This results from ad hoc manipulation of set size to get the results you want.

We should leave that sort of non-scientific ad hoc data manipulation to conspiracy theorists and climate change deniers