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A workor for the Chicopo Park District removes the sign of the park on West Ogdan les 506 Chapter To Markov Chains (e 10 years Id 10 32. Market A markere sody Was ning . W Melihood chut alamily woche y te follawine w y cerpent only (DX sa pomernly gent and a powder and it is the found that purchases from week tawek couli. be well the foewing nositi matrix D N D P B 06724 DOBS7 0.5226 02190 00367 07179 00444 DIN * 0.1235 0.2407 05123123 N 6.1465 4.2584 0029 0.572 1 11 al 3021 Applications Business and Economics 28. Cell Phones In Example 1, the following transition was determitt for customers upending their cell phones Mer Phone 4 40 Current Phone 035 0.65 # ) Suppose that each timer upgrades to a new cell phone every o years. Use as powers of the transition matrix to find the probability that a customer who currently owns Phone A will select Phone A for the following upgrade ia) Fint upgrade ib) Second upgrade c) Third upgrade d What is the probability that castomer bo cumuntly has () a Phone B will select Phone A for the second upgrade? 29. Cell Phones Suppose that Phone Ahns a 40% marke sure initially, with Phone B having a 60% share. Use the transition matrix from lixercise 28 find the nike share for each phane after each of the following upgrades. (a) First upgrade (b) Seccod upgrade (c) Third upgrade 30. Insurance An Insurance company classifies its divers into three groups: Go to Accidents), G, one sceident, and Gs Canare than one accident. The probability that driver will remain ay after year is 0.75, that the diver will become a is 0.20 and that the he will become a Cs is 0.08. A driver cannot become a Ghis company has a long memory, Thero is a 0.20 probability that a driver will canaina | AG driver must remain a G (a) Write a transition marx using this information (h) Suppose that the company cuents 50,00 new palicy holders, all of whom are divers. Find the number is each group alter the following time periods (i) 1 year ( 2 years (iii3 (in 3 years (1) 4 yenes 31. Insurance The difficulty with the mathematical model in Exercise 30 is that no "prave period is provided; thicrescu be a certain positive probability of muvity from or buck to G A new system with this feature night produce thic to ing transition matrix. We weeks In the land se paremier the topics le) Write the transition milik for ata period in Lever resulstrom part to the city idle plot of land is still 3. Businesti The Change in tim Size of Cancimetan be Markov chain. The bus at last three nes based on a 2-10 cmpirytal, medium 11-13 employees), and aru 44 Or more employees. There insteix for alycard is given below Small Me La Small 0.9216 0.000000 De 408959 0051 Large Lo 003 002 0 Suppose that in 2020, he were 2194 small, 2763 medium, nud 2278 Inrye businesses Botins de find the num ber of businesses of each type that would be expected in each of the fullmving seas. Source Applied Statistics. b) 222 Ich Wote the transition mateix for a 2 years Based on your answer. What proof medium busi Desses are in each of the listiroine Calegories after 2 years? Td Sual hasics lel La veces * Queuing Chain In the manne chain, we sulle til peuple ane yucwing up to be served by say, a bank teller. For simplicity Ict us assure that new people in me, no one else can enter the inc. Istos further assume thar on pason is ac cvery minut, as long as ren is in line Acme is that in a minute, there is a chility 12 that in omnem the line, a probability of 1/3 than exactly one personlitsus line, and a probbility 16 thully www people the the liac, ting there is nom. If there is not tooh om for two pexiple, then the truthnility that coc personen the line is 1/2 at the state he viven by the number of people in line a) Verily that the initiation B1 0 1 2 0 1 In Le week 22 of the holes wys y, A only, 415 Cod powder seduta! neither. Soure: Journal of Marketing Research 1) Padth. probability vector for the counr work thy Find the probability vector for the third we (e) Find thic transition tarix fora.wo-werker ( Using your answer from parc. find the problemy Tally using detcrgent ay is stag driceportal 33. Solar Energy A LOLIY A su galot to the carbon footprint in 10 yers. As part of the Green chimpien, they have offered becis incentives to come Lo solar energy for home healing County leaders Car vine 53 of rase who usc clotrichent and US nowo use fossil fuels la convert to startar al Llena calize that some homerater W. X xerite and ther 55 oflimuse whouse electric heal wil instead over to sihick wielc 15% of those who ase fossil fuels will civerboruri hen. Of those who use solar energy whilerrisin Iar enery: (al Waste transition mix lexing this informativ, abalina the masaxlexium C. and the clocicio.us mlar, respectively. A. the beginning of the cupaign. 156. of heancew: UX: electric heat, al use fxsilimdonly 55 use sur le Fin L nurther il merwners using cach typ batte the following lime geries (b) year (c) 2 years (d) Iveta Ftel The goal of the country leaders is to have at leasts Gifhorcow.costing solar energy liv bare herring in years. Ithis trend continues, will be not their call How to my years will it take any chevet is goal 34. Land Use lane witc. Bart of Realtors and asc SUV shxwed that 55 of all and was used for acrilicales while I was war. Ten years later of the writibarad 15 hud becue xerized aml OS had cridge tural (l'he remainder lay dle: the idic lm, 205 ! occane denized and had been cierdie agricultural se. Of the urban land, warenedaban and IOS aside Asute that these Inenda curtiue. (a) Write a trust matrix ask this incoration (b) Write a probability vector for the initial distribution 2 0.75 0.20 0.051 0.10 0.71 0.21 Lato 030 0.00 by Find the transitionatrix for a 1-minuteneriod le Use your result item part (b) find the probability a queue with no one in line has to people in line 2 utes later. Suppose that when this new policy is adopted, the company has 50.00 policyholders, all in G. Find the number in each group after the following time periods. (a) 1 year (b) 2 years (e) 3 years (d) Write the transition matrix for a 2 year period. (e) Use your result from purt (dita find the probability that a delver in G is soll in G, two years later Life and Health Sciences 37. Immune Response A study of imune response in cam classified the rabbits into fos grup, Scording to this of the response. From toe week to the next, the calibitsche Classification from one group to soother according to the ing transition mattis. Source: Journal of Thewetiral Biol C A workor for the Chicopo Park District removes the sign of the park on West Ogdan les 506 Chapter To Markov Chains (e 10 years Id 10 32. Market A markere sody Was ning . W Melihood chut alamily woche y te follawine w y cerpent only (DX sa pomernly gent and a powder and it is the found that purchases from week tawek couli. be well the foewing nositi matrix D N D P B 06724 DOBS7 0.5226 02190 00367 07179 00444 DIN * 0.1235 0.2407 05123123 N 6.1465 4.2584 0029 0.572 1 11 al 3021 Applications Business and Economics 28. Cell Phones In Example 1, the following transition was determitt for customers upending their cell phones Mer Phone 4 40 Current Phone 035 0.65 # ) Suppose that each timer upgrades to a new cell phone every o years. Use as powers of the transition matrix to find the probability that a customer who currently owns Phone A will select Phone A for the following upgrade ia) Fint upgrade ib) Second upgrade c) Third upgrade d What is the probability that castomer bo cumuntly has () a Phone B will select Phone A for the second upgrade? 29. Cell Phones Suppose that Phone Ahns a 40% marke sure initially, with Phone B having a 60% share. Use the transition matrix from lixercise 28 find the nike share for each phane after each of the following upgrades. (a) First upgrade (b) Seccod upgrade (c) Third upgrade 30. Insurance An Insurance company classifies its divers into three groups: Go to Accidents), G, one sceident, and Gs Canare than one accident. The probability that driver will remain ay after year is 0.75, that the diver will become a is 0.20 and that the he will become a Cs is 0.08. A driver cannot become a Ghis company has a long memory, Thero is a 0.20 probability that a driver will canaina | AG driver must remain a G (a) Write a transition marx using this information (h) Suppose that the company cuents 50,00 new palicy holders, all of whom are divers. Find the number is each group alter the following time periods (i) 1 year ( 2 years (iii3 (in 3 years (1) 4 yenes 31. Insurance The difficulty with the mathematical model in Exercise 30 is that no "prave period is provided; thicrescu be a certain positive probability of muvity from or buck to G A new system with this feature night produce thic to ing transition matrix. We weeks In the land se paremier the topics le) Write the transition milik for ata period in Lever resulstrom part to the city idle plot of land is still 3. Businesti The Change in tim Size of Cancimetan be Markov chain. The bus at last three nes based on a 2-10 cmpirytal, medium 11-13 employees), and aru 44 Or more employees. There insteix for alycard is given below Small Me La Small 0.9216 0.000000 De 408959 0051 Large Lo 003 002 0 Suppose that in 2020, he were 2194 small, 2763 medium, nud 2278 Inrye businesses Botins de find the num ber of businesses of each type that would be expected in each of the fullmving seas. Source Applied Statistics. b) 222 Ich Wote the transition mateix for a 2 years Based on your answer. What proof medium busi Desses are in each of the listiroine Calegories after 2 years? Td Sual hasics lel La veces * Queuing Chain In the manne chain, we sulle til peuple ane yucwing up to be served by say, a bank teller. For simplicity Ict us assure that new people in me, no one else can enter the inc. Istos further assume thar on pason is ac cvery minut, as long as ren is in line Acme is that in a minute, there is a chility 12 that in omnem the line, a probability of 1/3 than exactly one personlitsus line, and a probbility 16 thully www people the the liac, ting there is nom. If there is not tooh om for two pexiple, then the truthnility that coc personen the line is 1/2 at the state he viven by the number of people in line a) Verily that the initiation B1 0 1 2 0 1 In Le week 22 of the holes wys y, A only, 415 Cod powder seduta! neither. Soure: Journal of Marketing Research 1) Padth. probability vector for the counr work thy Find the probability vector for the third we (e) Find thic transition tarix fora.wo-werker ( Using your answer from parc. find the problemy Tally using detcrgent ay is stag driceportal 33. Solar Energy A LOLIY A su galot to the carbon footprint in 10 yers. As part of the Green chimpien, they have offered becis incentives to come Lo solar energy for home healing County leaders Car vine 53 of rase who usc clotrichent and US nowo use fossil fuels la convert to startar al Llena calize that some homerater W. X xerite and ther 55 oflimuse whouse electric heal wil instead over to sihick wielc 15% of those who ase fossil fuels will civerboruri hen. Of those who use solar energy whilerrisin Iar enery: (al Waste transition mix lexing this informativ, abalina the masaxlexium C. and the clocicio.us mlar, respectively. A. the beginning of the cupaign. 156. of heancew: UX: electric heat, al use fxsilimdonly 55 use sur le Fin L nurther il merwners using cach typ batte the following lime geries (b) year (c) 2 years (d) Iveta Ftel The goal of the country leaders is to have at leasts Gifhorcow.costing solar energy liv bare herring in years. Ithis trend continues, will be not their call How to my years will it take any chevet is goal 34. Land Use lane witc. Bart of Realtors and asc SUV shxwed that 55 of all and was used for acrilicales while I was war. Ten years later of the writibarad 15 hud becue xerized aml OS had cridge tural (l'he remainder lay dle: the idic lm, 205 ! occane denized and had been cierdie agricultural se. Of the urban land, warenedaban and IOS aside Asute that these Inenda curtiue. (a) Write a trust matrix ask this incoration (b) Write a probability vector for the initial distribution 2 0.75 0.20 0.051 0.10 0.71 0.21 Lato 030 0.00 by Find the transitionatrix for a 1-minuteneriod le Use your result item part (b) find the probability a queue with no one in line has to people in line 2 utes later. Suppose that when this new policy is adopted, the company has 50.00 policyholders, all in G. Find the number in each group after the following time periods. (a) 1 year (b) 2 years (e) 3 years (d) Write the transition matrix for a 2 year period. (e) Use your result from purt (dita find the probability that a delver in G is soll in G, two years later Life and Health Sciences 37. Immune Response A study of imune response in cam classified the rabbits into fos grup, Scording to this of the response. From toe week to the next, the calibitsche Classification from one group to soother according to the ing transition mattis. Source: Journal of Thewetiral Biol C
