<t>QuoteOriginally posted by: JackBryana man put a letter into one of them with 50% randomly.This isn't very clear. Are you saying 50% of the time he decides to put a letter in the room, and given that he has decided to do this the location is chosen uniformly among the 8 drawers?P( "In Drawer 8" | ...

Why on earth would the odds matter? The question states a desired outcome for each possible case, the relative probability of the possible cases makes absolutely no difference. Sciencegeek says he makes the even odds assumption but doesn't actually even really use it in his tree calculation.

Glad it worked out for you.

<t>Your question is not state very clearly but here is my answer to what I think you're asking.You didn't state it explicitly but I think what you're getting at is that the arrival rate of uptown and downtown trains is in fact the same. But the fact that Tony gets on the first uptown train introduce...

<t>QuoteOriginally posted by: Traden4AlphaFor the second scenario, there's two possibilities:1. You originally picked the seat with the prize (P=0.001). Now none of the remaining 9 seats has the prize. Thus, your seat contains the prize.2. You originally picked the seat without the prize (P=0.999). ...

<t>Do it in a simpler case. Say there are 3 seats. Let "u" denote you and "p" the prize. The possible cases areu p | ......| ..... u ...| p ...| ..... u ...| ......| p .. ... p| u ...| ..... ......| u p | ..... ......| u ...| p .. ... p| ......| u .. ......| p ...| u .. ......| ......| u p So yes 1/...

No that's wrong.

Why don't you at least try to do what I said before asking for more help? Or read the article as suggested by bearish.

Apply Ito's Lemma to Yt e^t and integrate

<t>BTW this problem is completely equivalent to trying to solve for the temperature distribution in two semi-infinite rods with different conductivities which are in thermal contact at x=0. I'm positive that must be a problem someone has done before but brief googling didn't really produce any good ...

<t>I've thought a little about how to solve the FP equation related to this problem. The equation is given by (ugh sorry sigmas should be squared)I'll call the conditions at x=0 BCs even thought we don't really have a boundary there. As pointed out before we want continuity. The second BC can be der...

I think you might be able to take a Fourier transform ofBecause will transform to some sort of sum of delta functions and hence you should be able to convolve it with the transform of phi_prime_prime pretty easily.

This sorting network stuff is really interesting. I'll have to look at what Knuth wrote about it (volume 3 pp. 219-247 it seems).Wikipedia claims that the optimal depth is only known for N<= 10 though, so trying to figure it out for ~5000 might be overzealous.

QuoteI think the lower bound might be O(log(N!)/N) based on information content but the constrains on the comparison make this lower bound optimistic.Thats just log(N) using Stirling's approximation, isn't it?

Are you guys clear on what the algorithm's complexity you're even trying to compute? I'm not.