You seem to be obsessed with having a pedantic debate on statistics. I have absolutely no interest in that. If you want to CONSTRUCTIVELY discuss how public pools can be defended in an environment where people are actively trying to cheat them I would be very interested in seeing what you think.
Bitcoin mining *is* statistics. If you don't understand them, you don't understand mining.
As I said, pedantic.
And with a Ph.D in engineering and over a decade in semiconductors I can assure you I understand the statistics just fine.
I look forward to your analysis of what actions a pool should take to defend against exploitation by miners either intentionally withholding block solutions or operating defective hardware.