Consider the three competing grocery stores in town, T'San Grocery, 654 Grocery and Sunlight Grocery. Consider the transition probabilities below: From T'San 654 Sunlight T'San 0.65 0.15 0.10 To 654 0.15 0.80 0.15 Sunlight 0.2 0.05 0.75 a. Compute the steady-state probabilities for this three-state Markov process. What mad
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.Consider the three competing grocery stores in town, T’San Grocery, 654 Grocery and Sunlight Grocery. Consider the transition probabilities below: To To To From T'San 654 Sunlight T'San 0.65 0.15 0.2 654 0.15 0.80 0.05 Sunlight 0.10 0.15 0.75 a. Compute the steady-state probabilities for this three-state Markov process.b. What market share will each store obtain?Consider the three competing grocery stores in town, ABC Grocery, 123 Grocery and XYZ Grocery. Consider the transition probabilities TO From abc grocery 123 grocery xyz grocery ABC grocery 0.65 0.15 0.2 123 GROCERY 0.15 0.80 0.05 xyz grocery 0.10 0.15 0.75 a. Compute the steady-state probabilities for this three-state Markov process.b. What market share will each store obtain?
- The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.02 0.98 (a)Which brand appears to have the most loyal customers? Explain. MDA has the most loyal customers because ( ) %? stay with them and only ( ) %? switch to the other brand, as opposed to Special B where only ( )%? stay with them and ( )%? switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B?1=? MDA?2=?The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.04 0.96 (a) Which brand appears to have the most loyal customers? Explain. _____ has the most loyal customers because _____ % stay with them and only _____ % switch to the other brand, as opposed to _____ where only _____ % stay with them and_____ % switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B ?1= _____ MDA ?2= _____Suppose a government study estimates that the proability of successive generations of a rural family reamining in a rural area was .7 and the probability of successive generations remaining in a urban area was .9. Assuming a Markov chain applies to these facts, what is the steady state vector?
- A study of pine nut crops in the American southwest from 1940 to 1947 hypothised that nut production followed a Markov chain. The data suggested that if one year's crop was good, then the probabilities that the following year's crop would be good, fair, or poor were 0.08, 0.07, and 0.85, respectively; if one year's crop was fair, then the probabilities that the follow-ing year's crop would be good, fair, or poor were 0.09, 0.11, and 0.80, respectively; if one year's crop was poor, then the probabilities that the following year's crop would be good, fair, or poor were 0.11, 0.05, and 0.84, respectively. (a) Write down the transition matrix for this Markov chain. (b) If the pine nut crop was good in 1940, find the probabilities of a good crop in the years 1941 through 1945. (c) In the long run, what proportion of the crops will be good, fair, and poorConsider the three grocery stores, Murphy’s Foodliner, Ashley’sSupermarket and Quick Stop Groceries. Quick Stop Groceries is smaller than eitherMurphy’s Foodliner or Ashley’s Supermarket. However, Quick Stop’s convenience withfaster service and gasoline for automobiles can be expected to attract somecustomers who currently make weekly shopping visits to either Murphy’s or Ashley’s.Assume that the transition probabilities are as follows: What is the projected market shares for the 3 convenient stores?Consider the following transition matrix of a Markov process. What is the steady-state probability of state 2?