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#6451 Re: Help Me ! » Markov Chains Problem » 2005-05-27 01:06:07
Indeed, if you are looking at one car owner, he will be on his "6 Year car" even after 8 years !
But we are looking at a large population here, I imagine, who are changing their cars every day.
Possible future for Large Car Owners (Year 0,3 and 6):
LLL
LLS
LSL
LSS
The question is for just one car owner, though. But it does not say how long the owner has had his present car.
So, he/she may exchange his car later today! Or not for 3 years.
#6452 Re: Help Me ! » Markov Chains Problem » 2005-05-27 00:35:47
Just for Fun, I worked out that matrix "P" where
P^3 = [0.6 0.25]
[0.4 0.75]
It is (approximately):
[0.818 0.114]
[0.182 0.886]
So, what is P^6 ?
[0.460 0.338]
[0.540 0.662]
And P^8 is:
[0.422 0.362]
[0.578 0.638]
And P^9 is
[0.411 0.369]
[0.589 0.631]
There is some drift due to calculation accuracy, but if you worked P out more accurately you may have something workable. But there may well be a rigorous way to do this rather than my "hey, lets use Excel and see what we get" approach 
#6453 Re: Guestbook » uiio » 2005-05-26 23:07:47
thanks!
#6454 Re: Help Me ! » Markov Chains Problem » 2005-05-26 22:27:51
OK, well, we still have your "8 year" problem ...
... you could cheat and work out the probabilites at 6 and 9 and ratio in between.
Or, you could work out an equivalent matrix that works on 1 year intervals.
In other words, what is the Matrix "P" where:
P^3 = [0.6 0.25]
[0.4 0.75]
(This is just an off-the-cuff idea, may not be rigorous)
#6455 Re: Help Me ! » Markov Chains Problem » 2005-05-26 22:21:20
Hi, maths_buff.
Markov chains are not my specialty, I am hoping that Milos or one of the other members is better versed in these than I am.
Having said that, I think your probability matrix needs to be transposed:
L S
S = L [ 0.6 0.25 ]
S [ 0.4 0.75 ]
So, if someone owns a large car at time 0 we will have
x(0) = [1]
[0]
at time 1 (3 years hence):
x(1) = [ 0.6 0.25 ] [1] = [0.6]
[ 0.4 0.75 ] [0] [0.4]
at time 2 (6 years hence):
x(2) = [ 0.6 0.25 ]^2 [1] = [ 0.46 0.3375 ] [1] = [0.46]
[ 0.4 0.75 ] [0] [ 0.54 0.6625 ] [0] [0.54]
(Which has the values you had already mentioned)
#6456 Re: Puzzles and Games » Horse race » 2005-05-26 21:10:27
Faaar Out!
You showed it!
#6457 Re: Guestbook » Thanks... » 2005-05-26 21:08:34
Big Smile 
#6458 Re: Puzzles and Games » Hi? » 2005-05-26 19:02:43
Oooohh .. a PUZZLE !
(6*6+6)/6 = 7 ...no
(6+6)/6 + 6 = 8 ...no
#6459 Re: Guestbook » algebra » 2005-05-26 11:05:32
We can help you - can you be more specific?
#6460 Re: Guestbook » Maths » 2005-05-26 09:48:28
Thank you so much! That makes me so happy to read.
#6461 Re: Help Me ! » Last one hopefully » 2005-05-26 09:45:22
cool_me, you are genius ...
... I think 
#6462 Re: Jokes » Jokes » 2005-05-26 09:41:03
LOL !!
#6463 Re: Maths Is Fun - Suggestions and Comments » Can we have a "general discussion" forum? » 2005-05-26 09:33:43
Vote:
The Mad Mathematicians Muddlings
Dark Discussions
Fun Forum
The Hangout
Cafe Infinity
The Set of All Topics
#6464 Re: Puzzles and Games » Horse race » 2005-05-26 00:52:39
Go on, draw the lines, then!
#6465 Re: Maths Teaching Resources » Crazy Teachers » 2005-05-26 00:07:39
Just as soon as they wake up!
#6466 Re: Help Me ! » Problem » 2005-05-25 21:37:28
The guys who posed it said "yes you can use the main signs add subtract multiply, divide not to sure weather too treat it as a logic problem?"
It seems to me that "Logic Problem" is a clue. It may not be solvable, I don't know.
#6467 Re: Introductions » sorry guys » 2005-05-25 09:43:35
answer = tin/cow
#6468 Re: Help Me ! » Puzzling Puzzle » 2005-05-25 09:41:42
Is that right? LOL !!
Do I get a prize for answering it, then?
#6469 Re: This is Cool » this is fun » 2005-05-25 09:34:45
Perhaps if we used some Algebra on it
Start With: 1+1=x
Subtract x from both sides: 1+1-x=x-x
Subtract 1 from both sides: 1+1-x-1=x-x-1
Simplify: 1-x=-1
I think that is as far as I can simplify it.
#6470 Re: Puzzles and Games » Horse race » 2005-05-25 09:30:45
"Think Outside The Square!"
#6471 Re: Guestbook » hiya:d:p » 2005-05-25 09:29:12
And thank YOU very much for taking the time to write such a nice note.
#6472 Re: Guestbook » Mr Underdown Yay!!!!!!!!!! » 2005-05-25 00:28:20
He must be a good teacher to have such a nice recommendation.
#6473 Re: Help Me ! » Problem » 2005-05-24 23:10:40
Rats, you mean it isn't solved?
Well, then, we shall try harder ...
#6474 Re: Guestbook » Maths » 2005-05-24 21:32:16
We can ALL help you, rivali. Just ask a question!
#6475 Re: Help Me ! » Puzzling Puzzle » 2005-05-24 18:30:31
Like this? No, sorry.
