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baddinlol

  • 2 years ago

I can't get the right answer for this probability question

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  1. baddinlol
    • 2 years ago
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    I must use transition matrices

  2. baddinlol
    • 2 years ago
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    The question is; an internet company has 80% of its customers on a dial plan and 20% of the cable plan

  3. zordoloom
    • 2 years ago
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    Can you just put the whole question out, instead of writing in small segments.

  4. baddinlol
    • 2 years ago
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    Ok sorry

  5. zordoloom
    • 2 years ago
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    No worries, it just helps to refer to one post instead of searching each post for parts of a question.

  6. baddinlol
    • 2 years ago
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    An internet company has 80% of its customers on a dial plan and 20% of the cable plan. They decide to bring out a deal which the market manager estimates each month, 20% of the customers on the dial up plan will change to the cable modem plan and 5% of the customers on the cable plan will change to the dial up plan. No customers will stop using the company. After four months, what proportion of the present customers will now be on the dial up plan?

  7. zordoloom
    • 2 years ago
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    Alright, does the question use numbers, or just percentages?

  8. baddinlol
    • 2 years ago
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    numbers

  9. zordoloom
    • 2 years ago
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    I mean, you just listed that there are 80% and 20%, do these percentages represent any numbers?

  10. baddinlol
    • 2 years ago
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    Oh no, they represent probablities

  11. baddinlol
    • 2 years ago
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    if you divide them by 100 i suppose

  12. zordoloom
    • 2 years ago
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    Thats fine, just use any number then. It would make the calculations easier.

  13. zordoloom
    • 2 years ago
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    So, say you have a total of 100 customers. 80% use dial up and 20% use cable

  14. zordoloom
    • 2 years ago
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    now after 1 month, 20% of the dial up customers will use the cable

  15. zordoloom
    • 2 years ago
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    and 5% will use dial up

  16. baddinlol
    • 2 years ago
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    yep

  17. zordoloom
    • 2 years ago
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    Okay, that would give you the data for 1 month

  18. zordoloom
    • 2 years ago
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    You want to continue doing this for 4 months.

  19. baddinlol
    • 2 years ago
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    But I must do the question using transition matrices

  20. zordoloom
    • 2 years ago
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    Thats fine, Do you know what a transition matrix is?

  21. baddinlol
    • 2 years ago
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    I tried setting up \[\left[\begin{matrix}0.8 & 0.2 \\ 0.05& 0.95\end{matrix}\right]\]

  22. baddinlol
    • 2 years ago
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    I multiplied that by itself 4 times

  23. zordoloom
    • 2 years ago
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    So far, it looks somewhat correct. You are missing

  24. baddinlol
    • 2 years ago
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    And then multiplied it by\[\left(\begin{matrix}0.8 \\ 0.2\end{matrix}\right)\]

  25. baddinlol
    • 2 years ago
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    And i got \[\left(\begin{matrix}0.471875 \\ 0.28203125\end{matrix}\right)\]

  26. zordoloom
    • 2 years ago
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    It would be set up a little differently.

  27. baddinlol
    • 2 years ago
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    How would i set it up?

  28. zordoloom
    • 2 years ago
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    The first row would include the percentages

  29. zordoloom
    • 2 years ago
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    sorry, column

  30. zordoloom
    • 2 years ago
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    and the next column would be the changes

  31. baddinlol
    • 2 years ago
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    Oh so columns have to add upto 100 (in terms of percentages)?

  32. zordoloom
    • 2 years ago
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    kinda, Its more like each row includes the number of variables. In this case there are 4 months.

  33. zordoloom
    • 2 years ago
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    So I would set up this matrix using a 4x4

  34. baddinlol
    • 2 years ago
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    Oh ok, thanks for your help =D

  35. zordoloom
    • 2 years ago
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    |dw:1351223751855:dw|

  36. zordoloom
    • 2 years ago
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    Just continue from here. Hope that somwhat helped

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