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Problem 3. (2 points) Consumers in Shelby ile have a choice of one of two fast food rostaurants, Krustys and McDonalds. Bot


Consumers in Shelbyille have a choice of one of two fast food restaurants, Krustys and McDonalds. Both have trouble keeping
Problem 3. (2 points) Consumers in Shelby ile have a choice of one of two fast food rostaurants, Krusty's and McDonald's. Both have trouble ke ping customers. Of those who last went to Krustys, 56% will go to McDonald's next time, and ofthose who last went to Mednars, 82% wil go to Krsty's next time. (a) Find the transition matrix describing this situation (assume that state 1 is Krusty's and state 2 is "McDonald's') (b) A customer goes out for fast food every Sunday, and just went to Krusty's What is the probability that two Sundays from now she will go to McDonald's? What is the probability that three Sundays from now she wil go to McDonald's? e Suppose a corsmer has k st moved to Shetyee and there is a 30% chance that he wil go to Krusty sfor No first fast 1ood outing what is the probabity that his third tast food e pere ee will be at Krusty's? (d) Find the steady-state probability vector. (Enter numbers that are accurate to at least 4 decimal places Note: You can eam partial credit on this problern.
Consumers in Shelbyille have a choice of one of two fast food restaurants, Krusty's and McDonald's. Both have trouble keeping customes. Or shose who last went to McDonald's next time, and of those who last went to McDonalds, 82% wa go to Krusty's not time. customers. Of those who last wert to Krusty's, 56% wil go to a) Find the transition matrix describing this stuation (assume that state 1 is "Knusty's" and state 2 is "McDonald's (b) A customer goes out for fast food every Sunday, and just went to Krusty's 0 What is the probability that two Sundays from now she will go to McDonald's? 0) What is the probability that three Sundays from now she will go to McDonald's? suppose a consumer has just moved to Shelbyvile, and there is a 39% chance that wil go to Knaty stor Ns frst tast food outr a what a the pot atity "at ha ind- food Krusty's7 (d) Find the steady-state probability vector (Enter numbers that are apcurate to at least 4 decimal places) Note: You can earn partial credit on this problem
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