what's the prob. that it is in the woods on 4th obervation?

2008-12-04 8:59 pm

Dear all,
I was wondering how to solve this math problem. Thank you very much!

If the animal is in the woods on one observation, then it is four times
as likely to be in the woods as the meadows on the next observation.
If the animal is in the meadows on one observation, then it is three times
as likely to be in the meadows as the woods on the next observation.

Assume that state 1 is being in the meadows and that state 2 is being in the woods.

(1) the transition matrix for this Markov process.
3/4 1/4
P=
1/5 4/5

(2) If the animal is in the woods on the first observation, what is the probability
that it is in the woods on fourth observation? (Express your answer either as a rational fraction or as a decimal fraction rounded to 4 decimal places.)
__________

Thank you very much!

回答 (1)

匿名

2008-12-05 6:50 am

✔ 最佳答案

Consider the following combination:

1: Woods, Woods, Woods, Woods
2: Woods, Woods, Meadows, Woods
3: Woods, Meadows, Woods, Woods
4: Woods, Meadows, Meadows, Woods

Pr (4th observation = Woods | 1st observation = Woods)
= Pr (1) + Pr (2) + Pr (3) + Pr (4)
= (4/5 x 4/5 x 4/5) + (4/5 x 1/5 x 1/4) + (1/5 x 1/4 x 4/5) + (1/5 x 3/4 x 1/4)
= 64/125 + 1/25 + 1/25 + 3/80
= 0.6295

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