For powerball to have an Expected Value of 1, the individual take-home jackpot would have to be about $313,124,412 for the lump sum, after taxes. (Which, assuming average state income tax rates, corresponds to an advertised jackpot of roughly $805,000,000 AND assumes the jackpot doesn't have multiple winners, which at that level is pretty unlikely.) Of course, since it's a risky bet, you don't want to blow your whole bankroll on lottery tickets even if the EV is above 1. That's where the Kelly Criterion comes in. According to the easy version of the Kel...
I asked... he apparently doesn't say much. She's theorizing Münchausen syndrome, which means he's not necessarily conscious that he's feigning illness.
Just as a completely non-religious example, my girlfriend is a medical social worker and has been working recently with a patient that is absolutely convinced he has cancer.
There has apparently been some cases of tests that came back clean, and his excuses after the fact, but it's also turned in to him anticipating future tests not finding the cancer, yet with him still certain he has cancer. I had originally suggested that she ask him ahead of time something like, "well if we do this test and it comes back clean, will you let it go?" but he wasn't even open to the question.
Is there a way to adjust this to support better scores for tighter confidence intervals?
For instance, using natural log, with a range of 8-10 and a true value of 10, I get -0.2231 whether I pick a 90% confidence interval, or a 95% confidence interval (coefficient of 40). It'd be nice if the latter scored better.