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Math Help - Matrix - transition problem2

  1. #1
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    Matrix - transition problem2

    If Regan passes his math test, the probability that he will pass the next one is 97%. If he fails his math test, the probability that he will pss the next one is only 85%
    Regan has worked hard on this unit so the probability that he will pass the first test is 95%

    a) Write the initial and the transition matrix
    b) What's the probability that Regan will pass the fifth test?

    The transition matrix would be
    0.97 0.03
    0.85 0.15

    the initial one...
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  2. #2
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    Re: Matrix - transition problem2

    Hi,
    yes ur transition matrix is correct.
    He will pass the first test,the intial probability distribution is given by A(0)=[1,0].
    The probability that regan will pass the fifth test is=A(0)p^4 [i.e if u take transition matix is p then find p^4 matrix]
    next u find the matix mltiplication for A(0) and p^4 u get the required result.
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  3. #3
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    Re: Matrix - transition problem2

    Regan has worked hard on this unit so the probability that he will pass the first test is 95%

    the initial shouldn't be [0.95,0.95]?
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  4. #4
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    Re: Matrix - transition problem2

    Quote Originally Posted by deepashree View Post
    Hi,
    yes ur transition matrix is correct.
    He will pass the first test,the intial probability distribution is given by A(0)=[1,0].
    The probability that regan will pass the fifth test is=A(0)p^4 [i.e if u take transition matix is p then find p^4 matrix]
    next u find the matix mltiplication for A(0) and p^4 u get the required result.
    No, the initial vector should be A(1) (not A(0) since the transition matrix only applies after he has taken a test) equal to [.95, .05]. And, since that is the probability vector for the first test, the probability that he will pass the first 5 tests is the first component of p^4A(1) (or A(1)p^4 depending upon your notation) where p is the transition matrix.
    Last edited by mr fantastic; September 24th 2011 at 05:43 PM. Reason: Added quote (I assume the post is in response to it) and fixed bold tag.
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  5. #5
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    Re: Matrix - transition problem2

    Thanks,
    Great explanations

    "In mathematics you don't understand things. You just get used to them." Johann von Neumann
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