Re: ISI 2017 key

Posted by ElPsyCongroo on May 16, 2017; 6:25am
URL: http://discussion-forum.276.s1.nabble.com/ISI-2017-key-tp7604137p7604190.html

Monkey question is related to random walk, you can google it online.

The second part I did not get but the first part I got to be 1 by elimination.

Basically I thought about the ways in which pi_1 could be true (that is, the monkey reaching 1 at some t>0).

So, that could be p (monkey moves right only) (1-p)^2(p)^3 (monkey moves two left and three right) and after this point I thought about a lot of other stuff but then that was not relevant to the answer. The moment you know pi_1 > p + (1-p)^2(p)^3, you can eliminate all options except the one for pi_k=1

Given p is greater than half and less than 1, then pi_1 can't be p^k, since that could imply pi_1 is p, but we know it's greater than p, ditto for the other option (I guess that was p/k) and for the option that said (p/(1-p))^k you can eliminate straight up because if p>1/2 this becomes  more than 1, and check the case for p=1/2 that will also give you something not possible.

Can't be zero also since pi_1 > p

So, it must be 1. There is a more formal solution, I found a pdf once, I'll post it here later if I find.