I have sample values coming from two truly random log normal distributions, A and B. They are continuous (analogue voltages actually). They are totally independent of one another, but theoretically identical in all aspects of size and shape. I then repetitively compare sample value A with sample value B, as in
IF valueA > valueB THEN RESULT = TRUE IF valueA < valueB THEN RESULT = FALSE
The comparison is done with analogue circuitry (not digital) so A = B cannot happen. What is the distribution of RESULT? I think that it has to be uniform. I think that it's effectively a Von Neumann extractor that will remove all bias /asymmetry from the log normal input distributions. Does anyone concur?