Or rather, undereducated semi-pro.

I’ve got a combinatorial optimization problem. It’s deterministic, and rather arbitrary, so don’t worry about the details.

There are a lot of feasible solutions. I drew a sample of 100000 solutions from the 82318282158320505 feasible ones, uniformly, i.i.d., all that stuff. “Random samples” say, and yes, I know that’s a loaded phrase.

The fitness/cost/performance of these 100000 samples appears to follow a normal distribution very nicely indeed. Yes, I know that’s a loaded phrase.

Say the average is 90000, and the measured standard deviation is 1000.

I know there are 82318282158320505 solutions.

Assuming the right stuff for this question to make sense: What’s the expected value of the lowest-cost (first) of the 82318282158320505 solutions?

I can look at MathWorld’s explanation of the Extreme Value Distribution(s) and the wikipedia bit on Order Statistics until I’m blue in the face and my head’s all tilty and like, “Wha?” but in the end, I am just a dumb ol’ biologist and can’t make the numbers and the equations click together.

I see that the formulae include places to stick whatcha call yer mean, and yer stad dev, and stuff. And an N, which is the number of samples you draw from said normal distribution. My N, she is too beeg.

Anybody?

Bueller?