Statistics simple and revised tree diagram

Question and data is given below!

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

Lakeshore Development Corporation LDC purchased land not far from the intersection of Highway 427 and The Queensway. The top managers of LDC , however, have different opinions on how this land can be used. Eventually, LDC commissioned preliminary architectural drawings for three different projects: Residential Towers; Mid-Rise Condos; Bungalow Complex. 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 LDC expectations are summarized in the following table (payoffs are in $millions). States of Nature Decision Alternatives Weak Strong Demand Demand Residential 29 -14 Towers Mid-Rise Condos 14 12 Bungalow 19 6 Complex Originally, LDC specialists counted on 0.66 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) = 0.66 , P(W) = 0, P1 = 29 , P2 = - 14, P3 = 14, PA = 12 , P5 = 19 , P6 = 6 Residential Towers Residential Towers Payoff 1 Payoff 4 P(S) P(W) Strong Mid-Rise Condos Weak Mid-Rise Condos O Payoff 2 Payoff 5 Bungalow Complex Bungalow Complex Payoff 3 Payoff 6P(S) = 0.66 , P(W) = 0.34, 191229.132 : 14,?3:14,P4=12,P5=19,P5=6 Residential Towers Payoff 1 13(3) Strong Mid-Rise Condos Payoff 2 Bungalow Complex Payoff 3 Residential Towers Payoff 4 KW) Weak Mid-Rise Condos Payoff S Bungalow Complex Payoff 6 P(S)=0.34,P(W)=0.66. 131229.132 214,193 219,194: 14,P5=12,P5=6 P( S) Siren Payoff 1 KW) Weak Residential Towers Payoff 3 KW) \\ Weak Payoff 4 Mid-Rise Condos P( S) Siren Payoff 5 PW) Weak Bungalow Complex Payoff 6 P(S)=0.66,P(W)=0.34, 191229.132 : 14,P3=14,P4=12,P5=19,P6=6 13(3) Strata Payoff 1 PM) Weak Payoff 2 33(3) Stron Payoff 3 PCW) Weak IResidential Towers Mid-Rise Condos Bungalow Complex Payoff None 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. 0 Find the expected monetary value for Residential Towers decision. 0 Find the expected monetary value for Mid-Rise Condos decision. 0 Find the expected monetary value for Bungal'ow Complex decision. (c) Using the simple decision tree determine the best decision policy. Construct Residential Towers if the demand is strong. Go ahead with Mid-Rise Condos project. Construct Residential Towers. Support Bungalow Complex project if the demand is strong. Support Bungalow Complex project. Go ahead with Mid-Rise Condos 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. Lakeshore Development Corporation managers are thinking about hiring Kanonhsa Research Group (KRG) to conduct a market research. Then, KRG 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 90% of cases when strong demand took place, KRG had predicted it correctly. It is also known that in 87% of cases when weak demand occurred, KRG had predicted it correctly. KRG 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 0.66 Weak 0.34 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 0.66 Weak 0.34 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(F) = 0.6382 , P(U) = 0.3618 P(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. P(F) = 0.9307 , P(U) = 0.8176 P(F)=P(Favorable Report) Hire Favorable Report Do not hire Residential Towers P(U)=P(Unfavorable Report) Hire In Do not hire branch Unfavorable Report use EMV of the optimal Do not hire decision alternative or include the whole decision tree from the Simple Decision Tree P(F)=P(Favorable Report) Hire part of the solution. Favorable Report Do not hire Mid-Rise Condos P(U)-P(Unfavorable Report) Hire Unfavorable Report Do not hire P(F)-P(Favorable Report) Hire Favorable Report Bungalow Complex P(U)-P(Unfavorable Report) Hire Unfavorable Report OP(F) = 0.628 , P(U) = 0.3816 P(F)=P(Favorable Report) Favorable Report Hire P(U)-P(Unfavorable Report) Unfavorable Report Residential Towers 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 O P(U)=P(Unfavorable Report) Unfavorable Report Mid-Rise Condos Do not hire P(F)=P(Favorable Report) Favorable Report Hire P(U)=P(Unfavorable Report) Unfavorable Report Bungalow Complex O Do not hire P(Hire) = 0.9 , P(Do not hire) = 0.87 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 None of the above. (g) Construct the revised decision tree and answer the following questions. Round all EMV answers to 2 decimal places. In case of favorable report, EMV(Residential Towers) = EMV( Mid-Rise Condos) S EMV(Bungalow Complex) = In case of unfavorable report, EMV(Residential Towers) = EMV( Mid-Rise Condos) EMV(Bungalow Complex) =. 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 KRG, please select N/A in case of favorable/unfavorable report. Select an answer + ] Kanonhsa 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 Lakeshore Development Corporation be willing to pay at most for the information about future economic conditions? If you recommend not hiring KRG, please enter zero in the answer cell. Keep 2 decimal places in the following answer. LDC can pay up to (in $ millions) (j) How efficient the KRG information would be? If you recommend not hiring KRG, please enter zero in the answer cell. Round your answer to 1 decimal place. Efficiency %