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Richard Weber 35p · 651 weeks ago
Anony · 651 weeks ago
Richard Weber 35p · 651 weeks ago
Let J be a 4x4 matrix of all 1s. Clearly, J has a set of linearly independent eigenvectors of (1,1,1,1), (-1,1,0,0), (-1,0,1,0),(-1,0,0,1), with eigenvalues of 4, 0, 0 ,0, respectively.
P = (1/3)(J-I), where I is the identity matrix. So any eigenvector of J is also an eigenvector of P. Hence the three eigenvectors of J with e-value 0, are eigenvectors of P with eigenvalue -1/3.
Clearly, this also works for a random walk on K_n (the complete graph on n vertices).
Vl@d · 649 weeks ago
I also believe there is a 'P' missing in the first line, before (H^A...|X_ 1=j)... Hope I'm not mistaking.
Richard Weber 35p · 649 weeks ago
There is no need for a t. We are using the idea that for a random variable Y taking values 1, 2, ... we can compute EY as sum_{t=1}^infty P(Y >= t).
Tadek Krassowski · 648 weeks ago
Richard Weber 35p · 648 weeks ago
Vl@d · 647 weeks ago
Richard Weber 35p · 647 weeks ago
If γ_k appears anywhere it is probably a misprint. Where did you see it?
Vl@d · 647 weeks ago
Thank you for clarifying that for me!
Richard Weber 35p · 647 weeks ago
anon · 637 weeks ago
JonnyTheStambledOne · 635 weeks ago
Few months ago I have stumbled upon some Markov chains. Last summer, I have red some interesting thing about it to. In high school I have red some things about it to.
My problem was when I analyzed the game of few people with the ball, each people have the probaliliti that will pass the ball to other person.
I got idea about multiple balls, and what if the game stoped if two balls are at one person, and also you could have the scenarion in witch U can have more balls in one person.
It could be the case that there is math developed for this, but I just dont know abut it....
If somebody know any thing about those subjects that I have mentioned above, I enurage it to writte to m;e...pleas..
ok it could be used in modeling Internet, servers, roads and so on....
anonymous · 634 weeks ago
http://www.manu-ao.ac.nz/massey/fms/Colleges/Coll...