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Math Help - Markov chain -state space and transition matrix

  1. #1
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    Markov chain -state space and transition matrix

    A beer vendor adopts the following stock replenishment policy: every Monday morning he
    buys fixed number N of six-packs of beer from the distributor, and sells the beer during the
    week. No matter how many packs he sells during that week, next Monday morning he will
    buy again N six-packs. Assume that the demand Dn for beer on week n is independent of the demand in previous weeks, and that its distribution is given by P(Dn=i) = di, i = 0, 1, 2, . . . (i is the number of six-packs).
    Let Xn be the number of beer packs in the store at the end of the nth week.
    Show that
    {Xn} is Markov chain, and determine its state-space and transition matrix.
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  2. #2
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    Mar 2010
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    Hint

    I have a starting hint that I think should be used for the problem:

    Xn can be defined as:
    Xn=Xn-1(starting inventory for week n)+N(no of 6 packs of beer purchased at the start of nth week)-Dn(Demand during week n)

    How do I go about finding the transition matrix for Xn and state space from here?
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