[graycat]

Yes, and it would be good to try to measure that effect also, and for that the statistics and optimization stand to be more difficult and advanced. E.g., the main input is not just some ads and clicks but a stochastic process, that is, random variables indexed by time.

Uh, go measure something and get a number. You now have the value of a random variable. The sense in which the number is random or unknowable in advance, unpredictable, independent of something else, etc. is left open. Collect such data once, say, over 3 months, and now have a sample path of the stochastic process. Do it again and get another sample path, etc.