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April 06, 2026, 01:01:29 pm
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Author Topic: Markov Chain 'n'  (Read 1542 times)  Share 

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kenhung123

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Markov Chain 'n'
« on: July 09, 2010, 05:39:20 pm »
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I remember from last year there was some questions relating to Markov chains that gave 'n' as not the power. Like 'normally' E.g. probably/number of X after 2 weeks then n=2 if the transition is on a weekly basis. But yea, does anyone know any examples where the number is not equal to the power?
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stonecold

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Re: Markov Chain 'n'
« Reply #1 on: July 09, 2010, 05:47:22 pm »
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Well they might give you the matrix for AFTER the first week, so to find the second week, n would just be equal to 1, and you would multiply it by the initial state matrix.
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the.watchman

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Re: Markov Chain 'n'
« Reply #2 on: July 09, 2010, 05:48:43 pm »
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Yeah, if they say something like:

Find the probability it snows on the second day, given that it rained on the first day

Then you'd use a power of 1, because it refers to the first day after the given event
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stonecold

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Re: Markov Chain 'n'
« Reply #3 on: July 09, 2010, 05:56:36 pm »
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does markov chains take up nearly a chapter of essentials? *please yes*
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kenhung123

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Re: Markov Chain 'n'
« Reply #4 on: July 09, 2010, 06:37:05 pm »
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Thanks a lot guys!

Also just wondering since the probability section in the text is so big, is it also big in the exam? I heard its small in the exam but the text book seems to disagree :P
Given that:
T=
S0=
what is d asking for? I thought T^50*?
« Last Edit: July 09, 2010, 06:49:56 pm by kenhung123 »
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stonecold

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Re: Markov Chain 'n'
« Reply #5 on: July 09, 2010, 07:05:33 pm »
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You have to be careful with those types of questions.  If it doesn't ask for a matrix, then you are simply required to answer in words.  Answers at the back of the book may not care, but VCAA will come end of year exam.

And I think you've done part d incorrectly.  You just take your proportions from part c, find the amount out of 3000, then express that as a fraction for each store.

And i'm 99% sure that is a Further question hehe!
« Last Edit: July 09, 2010, 07:07:14 pm by stonecold »
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kenhung123

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Re: Markov Chain 'n'
« Reply #6 on: July 09, 2010, 07:16:10 pm »
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Yea it is lol!
Umm, so %*3000/initial number at shop?
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stonecold

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Re: Markov Chain 'n'
« Reply #7 on: July 09, 2010, 07:18:45 pm »
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^umm, I think it's:

(%(each shop) x 3000)/3000

So three answers.

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TrueTears

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Re: Markov Chain 'n'
« Reply #8 on: July 09, 2010, 07:25:42 pm »
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Quote from: stonecold on July 09, 2010, 05:56:36 pm
does markov chains take up nearly a chapter of essentials? *please yes*
yes

Quote from: kenhung123 on July 09, 2010, 06:37:05 pm
Thanks a lot guys!

Also just wondering since the probability section in the text is so big, is it also big in the exam? I heard its small in the exam but the text book seems to disagree :P

yes
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kenhung123

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Re: Markov Chain 'n'
« Reply #9 on: July 09, 2010, 07:48:14 pm »
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Quote from: stonecold on July 09, 2010, 07:18:45 pm
^umm, I think it's:

(%(each shop) x 3000)/3000

So three answers.


Hmm the answer is 17/74, 9/24, 24/37. Your method works for shop A though.
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pooshwaltzer

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Re: Markov Chain 'n'
« Reply #10 on: July 09, 2010, 08:40:33 pm »
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I like this Q...
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kenhung123

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Re: Markov Chain 'n'
« Reply #11 on: July 10, 2010, 06:06:52 pm »
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What questions that O.o
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kenhung123

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Re: Markov Chain 'n'
« Reply #12 on: July 10, 2010, 09:12:57 pm »
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I have problem with this question also, I tried to do this
Column 1 is Victoria, column 2 is Queensland
Row 1 is stayed Row 2 is returned
to get the long term % net gain we use column 1 row 2 and column 2 row 2 percentages and multiply by 6000 and 400 respectively? i.e. we find the % staying in qld from vic and staying in vic from qld then find the numbers and subtract the number of people?

I am not sure if I made an incorrect assumption labeling row 1 and 2 as return and stayed other than return TO VIC and return TO QLD (however that would make it a 4x2 matrix with zero's...
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pooshwaltzer

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Re: Markov Chain 'n'
« Reply #13 on: July 10, 2010, 11:16:08 pm »
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annually net change = -6000(0.73)+400(0.1)
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kenhung123

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Re: Markov Chain 'n'
« Reply #14 on: July 11, 2010, 12:36:28 pm »
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The answer did this : 6000-772=5229 victorians to queensland. Could they be wrong because they didn't calculate the number that STAYED?
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