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baddinlol

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

  • one year ago
  • one year ago

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  1. baddinlol
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    I must use transition matrices

    • one year ago
  2. baddinlol
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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

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

    • one year ago
  4. baddinlol
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    Ok sorry

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

    • one year ago
  6. baddinlol
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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?

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

    • one year ago
  8. baddinlol
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    numbers

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

    • one year ago
  10. baddinlol
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    Oh no, they represent probablities

    • one year ago
  11. baddinlol
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    if you divide them by 100 i suppose

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

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

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

    • one year ago
  15. zordoloom
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    and 5% will use dial up

    • one year ago
  16. baddinlol
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    yep

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

    • one year ago
  18. zordoloom
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    You want to continue doing this for 4 months.

    • one year ago
  19. baddinlol
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    But I must do the question using transition matrices

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

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

    • one year ago
  22. baddinlol
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    I multiplied that by itself 4 times

    • one year ago
  23. zordoloom
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    So far, it looks somewhat correct. You are missing

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

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

    • one year ago
  26. zordoloom
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    It would be set up a little differently.

    • one year ago
  27. baddinlol
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    How would i set it up?

    • one year ago
  28. zordoloom
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    The first row would include the percentages

    • one year ago
  29. zordoloom
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    sorry, column

    • one year ago
  30. zordoloom
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    and the next column would be the changes

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

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

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

    • one year ago
  34. baddinlol
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    Oh ok, thanks for your help =D

    • one year ago
  35. zordoloom
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    |dw:1351223751855:dw|

    • one year ago
  36. zordoloom
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    Just continue from here. Hope that somwhat helped

    • one year ago
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