Transfer Matrix Interpretation

[jk22]

Hi, nice to meet you.

I'm trying to understand the formalism of transition matrices in probability :

a) if I have a state determined by (s1,...sr), where si is in {h,t} (head tail), the probability of head were p, and tail : q=1-p.

what Does the matrix :

mean :

s1 becomes head (p), and s2-sr becomes tail (q) ?

b) how to prove that : ?

thx.

[Martingale]

Hi, nice to meet you.

I'm trying to understand the formalism of transition matrices in probability :

a) if I have a state determined by (s1,...sr), where si is in {h,t} (head tail), the probability of head were p, and tail : q=1-p.

what Does the matrix :

mean :

s1 becomes head (p), and s2-sr becomes tail (q) ?

b) how to prove that : ?

thx.

is the last row in M supposed to just be [p,0,0...,0]?

is M supposed to be a Markov transition matrix?

is , times the vector ?

[jk22]

Hello,

yes, I read it like that. M is said to be a stochastic matrix.

[Martingale]

Hello,

yes, I read it like that. M is said to be a stochastic matrix.

then how can the bottom row be [p,0,...0]

shouldn't each row add to 1?

[jk22]

Hi,

if it were a sub-stochastic matrix, it wouldn't need this condition ?

thanks.

[Martingale]

Hi,

if it were a sub-stochastic matrix, it wouldn't need this condition ?

thanks.

Did you remove an absorbing state?