baddinlol
I can't get the right answer for this probability question
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baddinlol
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I must use transition matrices
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
zordoloom
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Can you just put the whole question out, instead of writing in small segments.
baddinlol
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Ok sorry
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.
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?
zordoloom
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Alright, does the question use numbers, or just percentages?
baddinlol
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numbers
zordoloom
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I mean, you just listed that there are 80% and 20%, do these percentages represent any numbers?
baddinlol
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Oh no, they represent probablities
baddinlol
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if you divide them by 100 i suppose
zordoloom
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Thats fine, just use any number then. It would make the calculations easier.
zordoloom
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So, say you have a total of 100 customers. 80% use dial up and 20% use cable
zordoloom
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now after 1 month, 20% of the dial up customers will use the cable
zordoloom
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and 5% will use dial up
baddinlol
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yep
zordoloom
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Okay, that would give you the data for 1 month
zordoloom
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You want to continue doing this for 4 months.
baddinlol
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But I must do the question using transition matrices
zordoloom
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Thats fine, Do you know what a transition matrix is?
baddinlol
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I tried setting up \[\left[\begin{matrix}0.8 & 0.2 \\ 0.05& 0.95\end{matrix}\right]\]
baddinlol
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I multiplied that by itself 4 times
zordoloom
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So far, it looks somewhat correct. You are missing
baddinlol
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And then multiplied it by\[\left(\begin{matrix}0.8 \\ 0.2\end{matrix}\right)\]
baddinlol
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And i got \[\left(\begin{matrix}0.471875 \\ 0.28203125\end{matrix}\right)\]
zordoloom
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It would be set up a little differently.
baddinlol
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How would i set it up?
zordoloom
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The first row would include the percentages
zordoloom
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sorry, column
zordoloom
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and the next column would be the changes
baddinlol
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Oh so columns have to add upto 100 (in terms of percentages)?
zordoloom
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kinda, Its more like each row includes the number of variables. In this case there are 4 months.
zordoloom
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So I would set up this matrix using a 4x4
baddinlol
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Oh ok, thanks for your help =D
zordoloom
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|dw:1351223751855:dw|
zordoloom
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Just continue from here. Hope that somwhat helped