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Interesting problem

Suppose you are listening to songs using xmms. And you allow a (almost uniform) random shuffle. There are 100 songs in your song list with each of duration t1, t2,..., t100. What is the estimated time
before song 42 is played?

I am going to hang around here till finally song 42 gets played. Whats worse, xmms's random shuffle doesn't seem all that random.

Comments

Chintan said…
hmm, the problem seems incomplete. Assuming perfect randomness from computers (a paradox in itself), song#i might not be played at all. You need additional restricting conditions and slightly re-framing the question. I think, what we can calculate is the probability that song#i is played within some fixed time 't'

Have left probability a long time back, so can't think of a strategy now but, the problem sounds interesting so will try to get back to it later.
2:33 PM
Anonymous said…
well its a trivial question. i solved such problems when i was 5 years old. it's simple. all u 've to do is to realize that the problem can be to mapped to the problem of constructing vector bundles in a mohovoric space with conical singularities. Then one can apply the usual vanishing theorem to obtian the result.

There is ofcourse the subtlietly of wheter mohorovic discontinuties are simple or of the fano variety type. However in this case one can show that the singularity is actually simple for which one has to simply use the well known restriction sequence of bundles on P_n. Then from this can see that the singularities are of the simple type. So finally after a very long calculation the answer turns out to be...

[\sqrt{t1t2...t100}]/
[exp{t1+t2+....t100}]
10:27 AM
Chintan said…
@anon: That doesn't make sense, AT ALL. How does seismology come into play here, wise guy!!
11:13 AM
Anonymous said…
I agree with Chintan. The anonymous has written some bluf instead of giving thought before writing.

I will try to think about solution for this problem. Interesting!
10:27 PM
Anonymous said…
dear chintan and the second anon. the permutation group P_n has a realization in algebraic geometry via the McKay correspondence, which you are both unaware of. So
it's not suprising that what i wrote in the comment went way above your head. I suggest you take some algebraic geom. courses before commenting on things you have no understanding of.

If you guys genuinely want to understand the solution i gave please ask me specific questions, instead of the rants you write here. For instance neither of you asked me why the answer i wrote is independent of t_24. This would have been a good question, which i'll be happy to explain if you are interested.
12:01 AM
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