ct4 Sept 2009 que7 (iv)

Discussion in 'CT4' started by Akansha, Sep 16, 2017.

  1. Akansha

    Akansha Active Member

    how to sketch the graph for this que? on what values this graph is sketched?
     
  2. John Potter

    John Potter ActEd Tutor Staff Member

    Hi Akansha,

    It tells you the axes in the question. Probabilities are between 0 and 1 for the y-axis, the x-axis is the number of times the car has been rented, label this 0, 1, 2, 3, etc.
    The probabilities for x=0 should be pretty obvious. If the car starts at the airport and has NOT been rented, it must be at the airport.
    Use your one-step and 2-step matrix from part (i). The top row gives you the probabilities, plot them on your graph. The stationary distribution in part (ii) then gives you the asymptotic behaviour of these probabilities. You could even calculate P^3 and P^4 to really see these probabilities head towards their long-term values (each time, it's the top row of your matrix). I would do this, it's good practice and consolidation of understanding Markov chains

    Good luck!
    John
     

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