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Math Help - Does all entries in a matrix of transition probabilities sum to 1 ?

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    Does all entries in a matrix of transition probabilities sum to 1 ?

    Does all entries in a matrix of transition probabilities sum to 1 ?
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    Re: Does all entries in a matrix of transition probabilities sum to 1 ?

    What is the definition of "matrix of transition probabilities"?
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    Re: 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"
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    Re: Does all entries in a matrix of transition probabilities sum to 1 ?

    You have a text book that asks questions about "Markov Processes" without telling you what a "Markov Process" is?
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    Re: Does all 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.
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    Re: Does all entries in a matrix of transition probabilities sum to 1 ?

    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 ?"
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    Re: Does all entries in a matrix of transition probabilities sum to 1 ?

    Quote Originally Posted by mathlearn View Post
    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 ?"
    It should be written somewhere in your book that each row of a transition probability matrix should sum up to 1.
    If the sum of each row and the sum of each column is equal to one, then your matrix is called a double stochastic matrix
    Last edited by harish21; September 20th 2012 at 07:06 PM.
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    Re: Does all entries in a matrix of transition probabilities sum to 1 ?

    Yea that I know that sum of all elements in a row is 1... but sum of all entries in transition probability matrix can't be 1 right ?
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    Re: Does all entries in a matrix of transition probabilities sum to 1 ?

    Quote Originally Posted by mathlearn View Post
    Yea that I know that sum of all elements in a row is 1... but sum of all entries in transition probability matrix can't be 1 right ?
    each row sums upto 1. So for a process with multiple states, the sum of all the entries of the matrix cannot be 1
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    Please delete this thread

    Please delete this thread
    Last edited by mathlearn; September 21st 2012 at 01:09 PM.
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    Re: Does all entries in a matrix of transition probabilities sum to 1 ?

    Quote Originally Posted by mathlearn View Post
    thank you for the explanation

    Since we are talking about matrix I wanna ask - When adding a square matrix, A, to its identity matrix, I, the sum is equal to matrix A ? or not ?
    \left[\begin{array}{cc}1&2\\3&4\end{array}\right]+\left[\begin{array}{cc}1&0\\0&1\end{array}\right]

    add the two matrices and see
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    Please delete this thread

    Please delete this thread
    Last edited by mathlearn; September 21st 2012 at 01:09 PM.
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