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In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less...

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 7%probability that a nonsmoker will begin smoking a pack or less per day, and a 3% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 6% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)

A) in 1 month

non-smokers --------------------------- people

1 pack/day or less---------------------people

more than 1 pack/day ----------------people

B) in 2 month

non-smokers --------------------------- people

1 pack/day or less---------------------people

more than 1 pack/day ----------------people

C) in 1 year

non-smokers --------------------------- people

1 pack/day or less---------------------people

more than 1 pack/day ----------------people

Solutions

Expert Solution

using markov transition matrix

from the given condition we have

P =   

and X0 =

after one month we have

X1 = * =

for second month

X2= X1*P

=  

after 1 year

X12= X0*P^12

Please rate if it has helped you

Thanks :)

milcah answered 2 years ago
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