Proof of Markov Chain: Bunny rabbit has three dens A, B and C. It likes A better than

coconi

New member
Joined
Oct 2, 2017
Messages
2
Hi all,

I have the following question in my assignment but I do not know how to proof:

Bunny rabbit has three dens A, B and C. It likes A better than B and C. If it's in B or C on
any night, it will always take chance 0.9 to go to A and chance 0.1 to go to the other den for the
following night. Once it reaches A, it will stay there for two nights and the third night will be in
B or C with equal chance 0.5. Let Xn be the stats Bunny is in for night n.

Question:
If the state space of the {Xn} is given by {First night at den A; Second night at den A; den B; den C}
then is {Xn} a MC?

Thanks.
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,356
Hi all,

I have the following question in my assignment but I do not know how to proof:

Bunny rabbit has three dens A, B and C. It likes A better than B and C. If it's in B or C on
any night, it will always take chance 0.9 to go to A and chance 0.1 to go to the other den for the
following night. Once it reaches A, it will stay there for two nights and the third night will be in
B or C with equal chance 0.5. Let Xn be the stats Bunny is in for night n.

Question:
If the state space of the {Xn} is given by {First night at den A; Second night at den A; den B; den C}
then is {Xn} a MC?

Thanks.
What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33
 

coconi

New member
Joined
Oct 2, 2017
Messages
2
What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

Hi Subhotosh,

Thanks. I would read the rules first.

Also, here is my idea:

To prove it it a MC, I may need to list all the possible conditional probability likes:

P(Xn+1 = "A" | Xn = "A", Xn-1 = "A") = 0 (Impossible to stay 3 nights)
P(Xn+1 = "A" | Xn = "A", Xn-1 = "B") = 1 (must stay 2 nights at A)
P(Xn+1 = "A" | Xn = "A", Xn-1 = "C") = 1 (must stay 2 nights at A)

So it is not a MC?
 
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