Wikipedia:Reference desk/Archives/Mathematics/2013 February 1

= February 1 =

Complex statistics
Is there any practical use for statistics done using complex numbers? --Carnildo (talk) 00:06, 1 February 2013 (UTC)
 * Yes. « Aaron Rotenberg « Talk « 02:05, 1 February 2013 (UTC)
 * I think that might be a misleading response, as although the wave function finds convenient representation in the complex numbers, none of the statistics (Bose–Einstein statistics, Fermi–Dirac statistics, Braid statistics) that arise from quantum mechanics make use of complex numbers. — Preceding unsigned comment added by 123.136.64.14 (talk) 02:46, 1 February 2013 (UTC)
 * OK, I need to stop giving one-word answers. I didn't mean that use of the word statistics. I meant that much of probability theory can be meaningfully reformulated using negative and complex amplitudes instead of probabilities, and that this can be applied to statistics in a practical way. For example, most quantum algorithms consist of initializing a quantum state, applying some transformations, and performing a measurement to get some probabilistic result. This is repeated many times, and the results are analyzed by applying some theorem that says that, given the sequence of manipulations applied and the particular statistic calculated, there is a high probability of getting the correct result. Naturally, in any practical quantum computer, you're going to need to apply some statistical reasoning to come up with a single result and make sure your results aren't contaminated. You could argue that it's pushing the boundaries of the wording, since the part that uses complex numbers directly is more probability theory than statistics, and it's not currently "practical". But it was the first thing that came to mind when putting the two concepts together in my head. « Aaron Rotenberg « Talk « 05:56, 1 February 2013 (UTC)
 * See also Bell's inequality for how you really do need complex numbers when finding probabilities. Dmcq (talk) 22:27, 1 February 2013 (UTC)
 * Perhaps the OP was interested in probability density functions defined over the complex numbers (that is, the support is the complex plane or a nonreal subset). Such functions cannot be analytic. There are complex generalizations of Gaussian distribution and Student's t distribution and the Wishart distribution but we only have articles on the first one, complex normal distribution AFAICS.  HTH, Robinh (talk) 22:49, 1 February 2013 (UTC)

Lottery
You're playing a game with a lottery where the cost of a ticket is $1. Each turn you have a random probability, p, of looking at how much money is in the pot. There is a also an unknown random chance of winning (w) the lottery every time someone enters, which would reset the pot to 0. It's also assumed that every time someone looks at the pot they must buy a ticket. Given p how many times do you have to look at the pot before you can get a good estimation of w? Is this answerable or do you need more information like how many people are playing the game? 70.162.4.242 (talk) 02:43, 1 February 2013 (UTC)
 * I think this may be answerable but I'm not sure I understood exactly the process, can you rephrase? -- Meni Rosenfeld (talk) 13:12, 1 February 2013 (UTC)
 * I read it as: you buy a ticket, one dollar is added to the pot, p chance of seeing the pot, w chance of winning the pot. You play again, having counted N players since your previous turn.
 * Another possibility is N persons playing in the same turn, in that case you can have more than one person winning, and splitting the pot I assume.
 * The first time you see the pot (M), chances are fifty-fifty of it being smaller or larger than average, so your inital estimate would be 1/(2M), no?Ssscienccce (talk) 14:56, 1 February 2013 (UTC)

Timezone
There is a computer program / website that can calculate time differences for me?--80.161.143.239 (talk) 18:32, 1 February 2013 (UTC)


 * Sure. Even Google can do it. Just type "Time in Moscow" (or wherever), without the quotation marks.  If you want to know relative differences and such, try http://www.timeanddate.com/worldclock/converter.html. StuRat (talk) 18:37, 1 February 2013 (UTC)