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 twice 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. If the animal is in the woods on the first observation, what is the probability that it is in the woods on fourth observation
what course is this for out of curiosity? Cause I could give you a linear algebra answer... but I feel like this is statistics
sounds like statistics to me too
it would make for a nice probability matrix question though... anyways, assuming this is statistics, I'd say first step is to write out your probabilities. just for the sake of keeping things a bit more concise, let the first capital letter be the starting location, and the second capital letter be the end location (ex: WM would be starting in the woods and ending in the meadow) if woods to woods is 4 times as likely as woods to meadow, then WW = 4*WM you also know that something has to happen and so the total of WW and WM = 100% you can solve for either and find that the probability of going from the woods to the meadow is 20% and the probability of going from the woods to the woods is 80% you can use the same thinking for starting in the meadow to find that MW = 1/3 and MM=2/3
then you have to carry these probabilities over 4 observations. this is a bit more straight forward with matrix multiplication, however i'll err on the side of caution and do straight probability. at observation 1, its in the woods (ergo 100% woods, 0% meadow) at observation 2 you have to multiply by the probabilities of going from the woods to either location. (1*80% woods, 1*20% meadow) then the same thing for observation 3 and 4, though this time you could potentially start in either woods or meadows so both come into play observation 3: (80%*80% + 1/3*20% chance of being in the woods, 20%*80% + 2/3*20% chance of being in the meadow) I'll let you try and do the last one! Good luck!
thanks for the help!
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