Thread: Stochastic Matrixes

Hello all. Its my first time posting so forgive any mistakes.

Got this problem in one of my reviews for a final this week, and can't quite figure it out. The prof kind of rushed this area and it didn't really settle in my mind. Tried it on my own for the past day and haven't been able to make much progress.

Anyway, here is the setup/question.

A group of physical fitness devotes works out in the gym every day .the Workouts vary from strenuous to moderate to light .when their exercise routine was recorded, the following observation was made: of the people who workout strenuously on a particular day, 40% will work out strenuously on the next day and 60% will work out moderately .of the people who work out moderately on a particular day, 50% will work out strenuously and 50% will work out lightly on the next day. Of the people working out lightly on a particular day, 30% will work out strenuously on the next day, 20% moderately, and 50% lightly.

a) Set up the 3x3 stochastic matrixes with columns and rows labeled S, M, and L that describes these transitions?

Now for this I have managed to get something, but not sure its correct.

[html]
S M L
S [.4 .5 .3
M .6 0 .2
L 0 .5 .5][/html]

b) Suppose that on a particular Monday 80% have a strenuous, 10% a moderate and 10% a light work out. What percent will have a Moderate work out on Tuesday?

This I'm confused about. If I'm right on the previous step, then deducing from previous work with matrices would indicate to get the answer for this I would have to multiply the matrix answer from question (a) with the column of .8 .1 and .1 that I would form from this question (b) to get the answer? I don't know if I'm even in the right neighborhood or just completely lost.

Any help at all would be greatly appreciated. I need to get this done asap and become familiar with it for the final this weekend. Once again, many thanks in advance for any who take the time to read through this. Only wish I would have found this forum earlier.

Originally Posted by Amsterdamn

Hello all. Its my first time posting so forgive any mistakes.

Got this problem in one of my reviews for a final this week, and can't quite figure it out. The prof kind of rushed this area and it didn't really settle in my mind. Tried it on my own for the past day and haven't been able to make much progress.

Anyway, here is the setup/question.

A group of physical fitness devotes works out in the gym every day .the Workouts vary from strenuous to moderate to light .when their exercise routine was recorded, the following observation was made: of the people who workout strenuously on a particular day, 40% will work out strenuously on the next day and 60% will work out moderately .of the people who work out moderately on a particular day, 50% will work out strenuously and 50% will work out lightly on the next day. Of the people working out lightly on a particular day, 30% will work out strenuously on the next day, 20% moderately, and 50% lightly.

a) Set up the 3x3 stochastic matrixes with columns and rows labeled S, M, and L that describes these transitions?

Now for this I have managed to get something, but not sure its correct.


[html]
S M L
S [.4 .5 .3
M .6 0 .2
L 0 .5 .5][/html]

that looks OK

b) Suppose that on a particular Monday 80% have a strenuous, 10% a moderate and 10% a light work out. What percent will have a Moderate work out on Tuesday?

This I'm confused about. If I'm right on the previous step, then deducing from previous work with matrices would indicate to get the answer for this I would have to multiply the matrix answer from question (a) with the column of .8 .1 and .1 that I would form from this question (b) to get the answer? I don't know if I'm even in the right neighborhood or just completely lost.

Yes that is right the matrix product will give the distribution of work out intensity for Tuesday, and the required answer will be the second element of the result.

CB

so, then it would be
[html]
S M L
S [.4 .5 .3 [.8 [.4
M .6 0 .2 .1 = .5
L 0 .5 .5] X .1] .1][/html]SO .5, or 50% would have a moderate workout on tuesday? Please let me know if this is correct. Thank you once again.