Does all entries in a matrix of transition probabilities sum to 1 ?
Not sure because I am trying to learn statistics (topic: Markov Process) and it has a statement which asks the reader if this it true or false "All the entries in a matrix of transition probabilities sum to 1"
Oh I am sorry, I thought you are asking me why I can;t answer this when I know the definition of "matrix of transition probabilities".
Based on my understanding from the reading the chapter from book, this is what I got:
Markov Process: A model used to analyze the evolution of a system over repeated trials when the state of the system at a given time cannot be determined with certainty.
State (of the system): The condition of the system at any particular trial or time period.
Transition Probability: The probability the system will be in state j during time period n+1 given that the system is in state i during time period n.
Markov Chain with Stationary Transition Probabilities:
A Markov Process in which:
Finite number of states
Transition probabilities remain constant
Probability of being in a particular state at any time period depends only on the state in the immediately preceding time period (memoryless property).
Transition Probabilities-
pij = probability of making a transition from state i in one period to state j in the next period.
P = matrix of transition probabilities.
State Probability πi(n) = the probability the system is in state i during period n.
Π(n) = [π1(n) π2(n) … πm(n)] = vector of state probabilities in period n.
There is no exact definition for the term "matrix of transition probabilities" - but that's what the question is that I am trying to answer if this statement is true or not "Does all entries in a matrix of transition probabilities sum to 1 ?"