Question

busisness analyasis markov chains

here is the question and answer. would like it broken down step by step

B Properties e Edit Links , Ted to g il Sort Filter Advanced Columns co Data Validation Manage Data Model Analyses-Sheet Forecast Data Tool Sort & Filter Connections Given the following vector of state probabilities and the accompanying matrix of transition probabilities, find the next period's state probabilities (ie market share) Use the Markov Chains method Original Market Shares at the beginning of the period 1 АВС 0.60 0.70 Predicted Market Shares for the end of the Period 1 0.50 0.30 0.20 0.50 Market Shares From the Period 1 0.60 0.00 0.00 0.00 0.1 10 0.70 Predicted Market Shares for the end of the Period 2 0.50 M1 Markov Content BUS 322 12 519 Samp 8 Bus 322 12 S19 Samplelems3219fsx-Exce View Add-ins ACROBAT PHStat Tel me what you want to do. Review Home Insert Page LayoutFormulas Flash Fi D Connections Show Queries From Table Redeh Relationships Manage Dats Model Anasis Shet ReapplyTet to - Remove Duplicates What- Forecant enal New Query Advanced Columms E0ta Vahdtion Forecast Data Teals Get & trandfer Sert & Given the following vector of state probabilities and the accompanying matrix of transition probablities, find the next period's state probabilities (i e market share). Use the Markov Chains method Predicted Market Shares for the end of the Period 1 0.3700 Original Market Shares at the begnring of the period 1 0.30 02600 0.3110 0.4110 0.2780 the Period 1 Predicted Market for the end of the 1.0000 BS 322 12 519

Answer 1

SOLUTION

Predicted propabilities are

0.5x0.6 + 0.3x0.1+0.2x0.2 = 0.3+0.03+0.04 =0.37

0.5x0.2+0.3x0.7 + 0.2x0.3 = 0.1+0.21+0.06 = 0.37

0.5x0.2+ 0.3x0.2+0.2x0.5 = 0.1 +0.06+0.1 = 0.26

phase2

0.37*0.6+0.37*0.1+0.26*0.2=0.222+0.037+0.052=0.311

0.37*0.2+0.37*0.7+0.26*0.3=0.074+0.259+0.078=0.411

0.37*0.2+0.37*0.2+0.26*0.5=0.074+0.074+0.13=0.278