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https://imathas.humber.ca/filestore/ufiles/291/STAT_2112_Instructions_to_Assignment_1_Summer_2022.pdf-

Toronto West Development Corporation TWDC purchased land not far from the intersection of Bloor Street West and Kipling Avenue. The top managers of TWDC , however, have different opinions on how this land can be used. Eventually, TWDC commissioned preliminary architectural drawings for three different projects: High-Rise Condo; Mid-Rise Apartments; Retirement Homes. Also, it is recognized that the financial success of the project depends on the situation on the real estate market, Strong Demand or Weak Demand. The TWDC expectations are summarized in the following table (payoffs are in $ millions). States of Nature Decision Alternatives Weak Strong Demand Demand High-Rise Condo 11 9 Mid-Rise 16 5 Apartments Retirement 26 -11 Homes Originally, TWDC specialists counted on 0.62 probability of strong demand. Simple Decision Tree Part (a) Suppose that you need to construct a simple decision tree that shows the logical sequence of the decision problem. Select the correct sketch of the decision tree based on the information above. Note that P(S)=probability of strong demand, P(W)=probability of weak demand. Also, we use the following notations: P1=Payoff 1, P2=Payoff 2 , P3=Payoff 3 , P4=Payoff 4 , P5=Payoff 5 , P6=Payoff 6 . P(S) = 0.62 , P(W) = 0.38, P1 = 11 , P2 = 9 , P3 = 16 , PA = 5 , P5 = 26, P6 = - 11 High-Rise Condo Payoff 1 P(S) Strong Mid-Rise Apartments Payoff 2 Retirement Homes Payoff 3 High-Rise Condo Payoff 4 P(W) Weak Mid-Rise Apartments C Payoff 5 Retirement Homes Payoff 6P(S) = 0.38 , P(W) = 0.62, P1 = 11 , P2 = 16 , P3 = 26 , PA = 9 , P5 = 5, P6 = - 11 P(S) Strong Payoff 1 High-Rise Condo P(W) Weak Payoff 2 P(S) Strong Payoff 3 O Mid-Rise Apartments P(W) Weak Payoff 4 P(S) Strong Payoff 5 Retirement Homes P(W) Weak Payoff 6 P(S) = 0.62 , P(W) = 0, P1 = 11 , P2 = 9, P3 = 16 , PA = 5 , P5 = 26, P6 = - 11 High-Rise Condo High-Rise Condo Payoff 1 Payoff 4 P(S) P (W) Strong Mid-Rise Apartments Weak Mid-Rise Apartments Payoff 2 Payoff 5 Retirement Homes Retirement Homes Payoff 3 Payoff 6 P(S) = 0.62 , P(W) = 0.38, P1 = 11 , P2 = 9, P3 = 16 , PA = 5 , P5 = 26 , P6 = - 11 P(S) Strong Payoff 1 High-Rise Condo C P(W) Weak Payoff 2 P(S) Strong Payoff 3 Mid-Rise Apartments O P(W) Weak Payoff 4 P(S) Strong Payoff 5 Retirement Homes O P(W) WeakNone of the above. [b] Using the sketch from the previous question and TreePIan, construct a simple decision tree. Based on the simple decision tree answer the following questions. Keep 2 decimal places in the EMU answers. I Find the expected monetary value for High-Rise Condo decision. I Find the expected monetary value for Mid-Rise Apartments decision. I Find the expected monetary value for Retirement Homes decision. (c) Using the simple decision tree determine the best decision policy. Go ahead with Mid- Rise Apartments project. Construct High-Rise Condo. Support Retirement Homes project. Support Retirement Homes project if the demand is strong. Construct High-Rise Condo if the demand is strong. Go ahead with Mid- Rise Apartments project if the demand is strong. None of the above. Revised Decision Tree Part The recent dramatic increase of the prime interest rate and still uncertain situation with COVID-19 affected the company's plans. Toronto West Development Corporation managers are thinking about hiring Mimico Research Group (MRG) to conduct a market research. Then, MRG would come up with either favorable report predicting strong demand, or unfavorable report predicting weak demand on the real estate market. It is known that in 80% of cases when strong demand took place, MRG had predicted it correctly. It is also known that in 85% of cases when weak demand occurred, MRG had predicted it correctly. MRG specialists need a month to complete their analysis, and they have to use expensive software, supercomputers, and hire additional computer and logistics analysts. (d) Suppose that you need to construct a revised decision tree. First, fill in the following revised probability tables for the favorable and unfavorable reports. Round joint probability values, P(Favorable), P(Unfavorable), and the posterior probability values to 4 decimals places. Probability Revisions given a Favorable Report State Prior Conditional Probability Posterior Probability of Probability P(Fav./State of Nature) Joint Probability P(State of Nature/Fav.) Nature Strong 0.62 Weak 0.38 P(Favorable) = 1.0000 Probability Revisions given an Unfavorable Report State Prior Conditional Probability Posterior Probability of Probability P(Unfav./State of Nature) Joint Probability P(State of Nature/Unfav.) Nature Strong 0.62 Weak 0.38 P( Unfavorable) = 1.0000 (e) Using the revised probability tables, please identify the revised/posterior probabilities which you are going to use in the revised decision tree: Keep 4 decimal places in the following answers. P( Strong demand | Favorable report ) = P( Weak demand | Favorable report) = P( Strong demad | Unfavorable report) P( Weak demand | Unfavorable report)(f) Now you start constructing the revised decision tree. Select the correct sketch of the leftmost part of the revised decision tree based on the information above. P( Hire) = 0.8 , P(Do not hire) = 0.85 Favorable Report P(Hire) In Favorable report Hire branch use EMV of the optimal decision Unfavorable Report alternative or include the whole decision tree O Favorable Report from the Simple Decision Tree part of P(Do not Hire) the solution. Do not hire Unfavorable Report P(F) = 0.8969 , P(U) = 0.7226 P(F)=P(Favorable Report) Hire Favorable Report Do not hire High-Rise Condo O P(U)=P(Unfavorable Report) Hire In Do not hire branch Unfavorable Report use EMV of the optimal Do not hire decision altemative or include the whole decision tree from the P(F)-P(Favorable Report) Hire Simple Decision Tree part of the solution. Favorable Report Do not hire Mid-Rise Apartments O P(U)=P(Unfavorable Report) Hire Unfavorable Report Do not hire P(F)=P(Favorable Report) Hire Favorable Report 0 Retirement Homes O P(U)=P(Unfavorable Report) Hire Unfavorable Report P(F) = 0.572 , P(U) = 0.416 P(F)=P(Favorable Report) Favorable Report Hire P(U)=P(Unfavorable Report) Unfavorable Report High-Rise Condo Do not In Do not hire branch hire use EMV of the optimal decision alternative or P(F)=P(Favorable Report) include the whole Favorable Report decision tree from the Simple Decision Tree part of the solution. Hire P(U)=P(Unfavorable Report) Unfavorable Report Mid-Rise Apartments O Do not hire P(F)=P(Favorable Report) Favorable Report Hire P(U)=P(Unfavorable Report) Unfavorable Report Retirement Homes O Do not hire P(F) = 0.553 , P(U) = 0.447P(F)=P(Favorable Report) Favorable Report The probabilities P(F) Hire and P(U) are calculated P(U)=P(Unfavorable Report) using the revised Unfavorable Report probability tables. Use EMV of the optimal decision Do not hire alternative or include the whole decision tree from the Simple Decision Tree part of the solution. None of the above. (9) Construct the revised decision tree and answer the following questions. Round all EMV answers to 2 decimal places. . In case of favorable report, EMV(High-Rise Condo) = EMV( Mid-Rise Apartments) EMV( Retirement Homes) . In case of unfavorable report, EMV(High-Rise Condo) EMV( Mid-Rise Apartments) EMV( Retirement Homes) . In the revised decision tree, there are the expected monetary values EMV(Hire) EMV(Do not hire) (h) Based on the revised decision tree formulate the optimal decision policy. Note that in each key word you have to use the scroll-down menu to select the correct option. If you recommend not hiring MRG, please select N/A in case of favorable/unfavorable report. Select an answer + ] Mimico Research Group. If their report is favorable, then choose the | Select an answer project. If the report is unfavorable, then go ahead with the | Select an answer *project.[i] How much would Toronto West Development Corporation be willing to pay at most for the information about future economic conditions? If you recommend not hiring MRG, please enter zero in the answer cell. Keep 2 decimal places in the following answer. TWDC can pay up to {in $ millions) [j] How efficient the MRG information would be? If you recommend not hiring MRG, please enter zero in the answer cell. Round your answer to 1 decimal place