math
posted by Sally .
A machine is either working (state 1) or not workind (state 2). If it is working one day the probability that it will be broken the next day is 0.1. If it is not working one day the probability that it will be working the next day is 0.8. Let Tn be the state of the machine n days from now. Assume the Markov assumption is satisfied so that Tn is a Markov Chain.
a) Give the transition matrix P for T.

If machine is working on day 0
prob working on day 1 = .9
prob broken on day 1 = .1
If machine is broken on day 0
prob working on day 1 = .8
prob broken on day 1 = .2
so
working broken 1 = working broken 0 *
.9 .1
.8 .2
for example if working day 0
(doing second row with / because of font text limitation here)
[W1 B1] = [ 1 0 } [ .9/.8 .1/.2 ]
= [.9 .1]
then
W2 B2 = [.9 .1][ .9/.8 .1/.2 ]
= [.81+.08 .09+.02 ]
= [.89 .11 ]
and
Wn Bn = [1 0] *
 .9 .8 ^n
 .8 .2 
Respond to this Question
Similar Questions

math
A machine is either working (state 1) or not workind (state 2). If it is working one day the probability that it will be broken the next day is 0.1. If it is not working one day the probability that it will be working the next day … 
math
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other … 
stat
a machine has 7 identical components which function independently. the probability that a component will fail is 0.2. the machine will stop working if more than three components fail. find the probability that the machine will be working. 
discrete probability distribution (help please!)
a machine has 7 identical components which function independently. the probability that a component will fail is 0.2. the machine will stop working if more than three components fail. find the probability that the machine will be working. 
Elementary Statistics
A machine has 7 identical components which function independently. The probability that a component will fail is .2. The machine will stop working if more than three components fail. Find the probability that the machine will be working? 
statistics
A widget factory's worker productivity is normally distributed. one worker produces an average of 75 widgets per day with a standard deviation of 20. another worker produces at an average rate of 65 per day with standard deviation … 
Markov chains
A company has 2 machines. On any day, each machine that is working has a 1/3 chance of breaking down. If a machine breaks down during the day, it is sent to a repair facility and will be working 2 days after it breaks down. Letting … 
linear algebra
The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been observed to be predictable largely on the basis of the weather on the previous day. Specfically: if it is sunny on one day, it will be sunny … 
Math probability
In a city, every day is either cloudy or sunny (not both). If it's sunny on any given day, then the probability that the next day will be sunny is 3/4. If it's cloudy on any given day, then the probability that the next day will be … 
math
A can do work alone in 15 days whereas B can destroy entire work in 20 days. They are working on alternate days with a working on the first day, B working on the second day, then how many days will work completed?