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#1 Re: Help Me ! » a probability question. » 2016-05-17 00:32:38
Thank you for your help, thickhead!
#2 Re: Help Me ! » a probability question. » 2016-05-14 19:10:40
Okay thanks, that was confusing me a bit!
Did you have any thoughts on the other questions?
EDIT: I get k=9/5(=1.8) when solving the first equation
#3 Re: Help Me ! » a probability question. » 2016-05-14 17:45:24
Hi thickhead,
F(y|1/2) is a conditional cdf of y on y=1/2 (at least I'm assuming the second part is y). Also for part a would we have to account for the case where x is negative?
Thanks!
#4 Re: Help Me ! » a probability question. » 2016-05-14 01:56:27
Hi thickhead,
I'm having trouble starting to calculate the cdf F(y|1/2), P(X<Y|Y>1/2), and E(X|Y>1/2).
Just wondering if you could show me how to do those after getting back to ChrIsPuZa?
Thanks!
#5 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-04-02 02:47:39
Then we can form the transition matrix where the rows tells the probabilities of moving to any room (columns).
Makes sense to me so far!
#6 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-30 02:03:53
Are you familiar with matrix operations?
Yes i am 
#7 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-29 12:01:51
From Room 2 to room 1 we assign 1 / 3 to room 2 we assign 1 / 3 and to room 4 we assign 1 / 3.
From Room 3 to room 1 we assign 1 / 3 to room 3 we assign 1 / 3 and to room 4 we assign 1 / 3.
From Room 4 to room 2 we assign 1 / 3 to room 3 we assign 1 / 3 and to room 4 we assign 1 / 3.
Makes sense so far
#8 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-25 20:17:46
Of course when we are speaking of the future we can only do so probabilistically.
We now have to assign probabilities for each room
From Room 1 to room 1 we assign 1 / 3 to room 2 we assign 1 / 3 and to room 3 we assign 1 / 3.
Sounds good!
#9 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-24 21:47:08
We decide we want to start with the mouse in the red room (room 1) so the initial vector will be
The experiment now consists of observing at regular fixed intervals of time the position and movement of the mouse. For example, after 1 such interval, the mouse could have stayed where he was or moved to either room 2 or room 3.
Sure thing
#10 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-21 22:18:29
You are getting ahead of yourself, are you ready with the example I have given to move on?
No worries, yes I am!
#11 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-21 00:20:45
I mean the space surrounding boxes 1, 2 and 3.
#12 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-19 15:57:56
The outside box is just a product of the cut and paste.
What is important is how the mouse moves through the rooms. He can go from 1 to 2 or 1 to 3 but not 1 to 4. He can also go from 3 to 4 and 3 to 1 but not 3 to 2 etc.
I meant the outside box in the initial maze diagram, the "fourth" room if you will
#13 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-19 01:07:05
To further clarify, the mouse can only move right - left or left-right and up-down or down up. No diagonal moves such as 1 to 4.
Does this account for the outside box then? As all boxes can be moved between directly (except for boxes 1 and 3).
#14 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-18 15:38:33
We now have a 4 rooms and a mouse, this is called the initial state.
We want to select a room for the mouse, if we agree that we would want to do this in an equally likely way then we form a row vector [1 / 4, 1 / 4, 1 / 4, 1 / 4]. If we always wanted the mouse to start in room 1 then we would form the row vector [1,0,0,0]. This vector is called the initial state vector.
Okay?
Sounds good
#15 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-17 19:36:05
We start with a maze of 4 rooms, each painted a different color and labeled 1,2,3 and 4. We wish to release a mouse into one of the rooms and observe its behavior. We would like to be able to predict the mouses movements in the maze.
http://i.imgur.com/LDJdMDY.png
Understand so far?
Looks good so far!
#16 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-17 03:15:51
I am basically a problem solver, (though not a good one), a teacher I am not. Are you sure you would not rather learn this technique using a somewhat simpler example?
If you had the time I would love for a simpler example to help increase my understanding before showing how it applies to this problem, but if you do not have time I would rather you showed me the way it applies to this question straight up. Thanks again!
#17 Re: Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-16 22:18:55
Hi;
Have you studied Markov chains yet?
Hi bobbym,
Unfortunately I have not, I looked through your example the last time you did this problem and I was having trouble seeing how it could apply to this problem, would it be okay if you guided me through step by step? I'd really like an intuitive understanding of how to do this question.
#18 Help Me ! » [Probability, University Introductory Level] "Rat Run" Question » 2016-03-15 23:46:25
- jakndaxta
- Replies: 27
A rat is released in the space outside a maze consisting of three rooms and six doors,
as depicted in the following figure.
Whenever the rat is in a space or room with k doors, it chooses each of these doors to move through next with probability 1/k. We are interested in the movement of the rat from when it first enters the maze until it first leaves.
(a) If the rat enters the maze at Room 1, find the probability that it will leave
from Room 3.
(b) If the rat starts in the space around the maze, find the probability that it will
eventually leave the maze from Room 3.
(c) If the rat leaves the maze from Room 3 find the probability that it entered at
Room 1.
(d) Suppose that the rat is now in the maze and we gain information which
makes us 70% confident that it entered at Room 1 and 20% confident
that it entered at Room 2, find the probability that:
(d.i) the rat will leave from Room 3
(d.ii) the rat entered at Room 1 if it leaves from Room 3
(d.iii) the rat entered at Room 1 if it leaves from Room 1.
For (d) it may be assumed that had we known at which room the rat entered the maze,
the said additional information would not alter our beliefs regarding subsequent movements of the rat.
Hi guys I'm currently trying to figure this question out, but I have no idea how to approach it. I came across a previous post on this question that utilised Markov Chains to calculate the probability of part (a) but I don't understand how its done.
I'd appreciate it if someone could walk me through completing at least part (a) and hopefully the rest of the question as well.
Thank you for your time!
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