An investment banker will choose 1 of 3 proposed investment strategies. The banker has modelled 4 possible scenarios in terms of global economic conditions that will determine the likely return for each of these investment strategies. The probability of each of the scenarios occuring is unknown. The following matrix $L$ represents the anticipated percentage returns with $L_{ij}$ giving the return for strategy $i \\in \\{1,2,3\\}$ under scenario $j \\in \\{1,2,3,4\\}$.
\n$L = \\var{L}$
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3"], "matrix": ["MMarks[2][0]", "MMarks[2][1]", "MMarks[2][2]"], "distractors": ["Maximum regret for strategy 1 is {Rmax[0]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 2 is {Rmax[1]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 3 is {Rmax[2]}. The minimum maximum regret is {Rminmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Hurwicz criterion with coefficient of optimism $\\alpha = \\var{alpha}$, which investment strategy would be chosen?
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\n$L = \\var{L}$
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[3][0]", "MMarks[3][1]", "MMarks[3][2]", "MMarks[3][3]"], "distractors": ["Hurwicz score for strategy 1 is {Hscore[0]}. The best score is {Hbest}.", "Hurwicz score for strategy 2 is {Hscore[1]}. The best score is {Hbest}.", "Hurwicz score for strategy 3 is {Hscore[2]}. The best score is {Hbest}.", "Hurwicz score for strategy 4 is {Hscore[3]}. The best score is {Hbest}."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Decision making under uncertainty (Investment Banker)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_jtnt3ZK.png", "/srv/numbas/media/question-resources/image_jtnt3ZK.png"], ["question-resources/image_YeZFAo0.png", "/srv/numbas/media/question-resources/image_YeZFAo0.png"], ["question-resources/image_OU9Lgsp.png", "/srv/numbas/media/question-resources/image_OU9Lgsp.png"], ["question-resources/image_unfUEiZ.png", "/srv/numbas/media/question-resources/image_unfUEiZ.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Corry", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/8910/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "An investment banker will choose 1 of 3 proposed investment strategies. The banker has modelled 4 possible scenarios in terms of global economic conditions that will determine the likely return for each of these investment strategies. The probability of each of the scenarios occuring is unknown. The following matrix $L$ represents the anticipated percentage returns with $L_{ij}$ giving the return for strategy $i \\in \\{1,2,3\\}$ under scenario $j \\in \\{1,2,3,4\\}$.
\n$L = \\var{L}$
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["strategy 1", "strategy 2", "strategy 3"], "matrix": ["MMarks[0][0]", "MMarks[0][1]", "MMarks[0][2]"], "distractors": ["Expected return for strategy 1 is {Lavg[0]}. The maximum expected return is {ELmax}.", "Expected return for strategy 2 is {Lavg[1]}. The maximum expected return is {ELmax}.", "Expected return for strategy 3 is {Lavg[2]}. The maximum expected return is {ELmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the MiniMax (MaxiMin) criterion, which investment strategies could be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3"], "matrix": ["MMarks[1][0]", "MMarks[1][1]", "MMarks[1][2]"], "distractors": ["Minimum return for strategy 1 is {Lmin[0]}. The maximum minimum return is {Lmaxmin}.", "Minimum return for strategy 2 is {Lmin[1]}. The maximum minimum return is {Lmaxmin}.", "Minimum return for strategy 3 is {Lmin[2]}. The maximum minimum return is {Lmaxmin}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Savage criterion, which investment strategies could be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3"], "matrix": ["MMarks[2][0]", "MMarks[2][1]", "MMarks[2][2]"], "distractors": ["Maximum regret for strategy 1 is {Rmax[0]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 2 is {Rmax[1]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 3 is {Rmax[2]}. The minimum maximum regret is {Rminmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Hurwicz criterion with coefficient of optimism $\\alpha = \\var{alpha}$, which investment strategy would be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3"], "matrix": ["MMarks[3][0]", "MMarks[3][1]", "MMarks[3][2]"], "distractors": ["Hurwicz score for strategy 1 is {Hscore[0]}. The best score is {Hbest}.", "Hurwicz score for strategy 2 is {Hscore[1]}. The best score is {Hbest}.", "Hurwicz score for strategy 3 is {Hscore[2]}. The best score is {Hbest}."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Decision making under uncertainty (Law Enforcement)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_jtnt3ZK.png", "/srv/numbas/media/question-resources/image_jtnt3ZK.png"], ["question-resources/image_YeZFAo0.png", "/srv/numbas/media/question-resources/image_YeZFAo0.png"], ["question-resources/image_OU9Lgsp.png", "/srv/numbas/media/question-resources/image_OU9Lgsp.png"], ["question-resources/image_unfUEiZ.png", "/srv/numbas/media/question-resources/image_unfUEiZ.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Corry", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/8910/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "The police comissioner will choose 1 of 4 proposed force deployment strategies for Brisbnae. The comissioner has modelled 3 possible scenarios in terms of 1. low, 2. medium and 3. high crime. The probability of each of the scenarios occuring is unknown. The following matrix $L$ represents the anticipated social cost of each strategy with $L_{ij}$ giving the cost for strategy $i \\in \\{1,2,3,4\\}$ under scenario $j \\in \\{1,2,3\\}$.
\n$L = \\var{L}$
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[1][0]", "MMarks[1][1]", "MMarks[1][2]", "MMarks[1][3]"], "distractors": ["Maximum cost for strategy 1 is {Cmax[0]}. The minimum max cost is {Lminmax}.", "Maximum cost for strategy 2 is {Cmax[2]}. The minimum max cost is {Lminmax}.", "Maximum cost for strategy 3 is {Cmax[2]}. The minimum max cost is {Lminmax}.", "Maximum cost for strategy 4 is {Cmax[3]}. The minimum max cost is {Lminmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Savage criterion, which strategies could be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[2][0]", "MMarks[2][1]", "MMarks[2][2]", "MMarks[2][3]"], "distractors": ["Maximum regret for strategy 1 is {Rmax[0]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 2 is {Rmax[1]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 3 is {Rmax[2]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 4 is {Rmax[3]}. The minimum maximum regret is {Rminmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Hurwicz criterion with coefficient of optimism $\\alpha = \\var{alpha}$, which strategy would be chosen?
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\n$L = \\var{L}$
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3"], "matrix": ["MMarks[1][0]", "MMarks[1][1]", "MMarks[1][2]"], "distractors": ["Minimum return for strategy 1 is {Lmin[0]}. The maximum minimum return is {Lmaxmin}.", "Minimum return for strategy 2 is {Lmin[1]}. The maximum minimum return is {Lmaxmin}.", "Minimum return for strategy 3 is {Lmin[2]}. The maximum minimum return is {Lmaxmin}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Savage criterion, which investment strategies could be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3"], "matrix": ["MMarks[2][0]", "MMarks[2][1]", "MMarks[2][2]"], "distractors": ["Maximum regret for strategy 1 is {Rmax[0]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 2 is {Rmax[1]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 3 is {Rmax[2]}. The minimum maximum regret is {Rminmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Hurwicz criterion with coefficient of optimism $\\alpha = \\var{alpha}$, which investment strategy would be chosen?
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\n$L = \\var{L}$
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[2][0]", "MMarks[2][1]", "MMarks[2][2]", "MMarks[2][3]"], "distractors": ["Maximum regret for strategy 1 is {Rmax[0]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 2 is {Rmax[1]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 3 is {Rmax[2]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 4 is {Rmax[3]}. The minimum maximum regret is {Rminmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Hurwicz criterion with coefficient of optimism $\\alpha = \\var{alpha}$, which strategy would be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[3][0]", "MMarks[3][1]", "MMarks[3][2]", "MMarks[3][3]"], "distractors": ["Hurwicz score for strategy 1 is {Hscore[0]}. The best score is {Hbest}.", "Hurwicz score for strategy 2 is {Hscore[1]}. The best score is {Hbest}.", "Hurwicz score for strategy 3 is {Hscore[2]}. The best score is {Hbest}.", "Hurwicz score for strategy 4 is {Hscore[3]}. The best score is {Hbest}."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Decision making under uncertainty (Investment Banker)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_jtnt3ZK.png", "/srv/numbas/media/question-resources/image_jtnt3ZK.png"], ["question-resources/image_YeZFAo0.png", "/srv/numbas/media/question-resources/image_YeZFAo0.png"], ["question-resources/image_OU9Lgsp.png", "/srv/numbas/media/question-resources/image_OU9Lgsp.png"], ["question-resources/image_unfUEiZ.png", "/srv/numbas/media/question-resources/image_unfUEiZ.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Corry", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/8910/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "An investment banker will choose 1 of 3 proposed investment strategies. The banker has modelled 4 possible scenarios in terms of global economic conditions that will determine the likely return for each of these investment strategies. The probability of each of the scenarios occuring is unknown. The following matrix $L$ represents the anticipated percentage returns with $L_{ij}$ giving the return for strategy $i \\in \\{1,2,3\\}$ under scenario $j \\in \\{1,2,3,4\\}$.
\n$L = \\var{L}$
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3"], "matrix": ["MMarks[3][0]", "MMarks[3][1]", "MMarks[3][2]"], "distractors": ["Hurwicz score for strategy 1 is {Hscore[0]}. The best score is {Hbest}.", "Hurwicz score for strategy 2 is {Hscore[1]}. The best score is {Hbest}.", "Hurwicz score for strategy 3 is {Hscore[2]}. The best score is {Hbest}."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Decision making under uncertainty (Law Enforcement)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_jtnt3ZK.png", "/srv/numbas/media/question-resources/image_jtnt3ZK.png"], ["question-resources/image_YeZFAo0.png", "/srv/numbas/media/question-resources/image_YeZFAo0.png"], ["question-resources/image_OU9Lgsp.png", "/srv/numbas/media/question-resources/image_OU9Lgsp.png"], ["question-resources/image_unfUEiZ.png", "/srv/numbas/media/question-resources/image_unfUEiZ.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Corry", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/8910/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "The police comissioner will choose 1 of 4 proposed force deployment strategies for Brisbnae. The comissioner has modelled 3 possible scenarios in terms of 1. low, 2. medium and 3. high crime. The probability of each of the scenarios occuring is unknown. The following matrix $L$ represents the anticipated social cost of each strategy with $L_{ij}$ giving the cost for strategy $i \\in \\{1,2,3,4\\}$ under scenario $j \\in \\{1,2,3\\}$.
\n$L = \\var{L}$
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[0][0]", "MMarks[0][1]", "MMarks[0][2]", "MMarks[0][3]"], "distractors": ["Expected cost for strategy 1 is {Lavg[0]}. The minimum expected cost is {ELmin}.", "Expected cost for strategy 2 is {Lavg[1]}. The minimum expected cost is {ELmin}.", "Expected cost for strategy 3 is {Lavg[2]}. The minimum expected cost is {ELmin}.", "Expected cost for strategy 4 is {Lavg[3]}. The minimum expected cost is {ELmin}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the MiniMax (MaxiMin) criterion, which strategies could be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[1][0]", "MMarks[1][1]", "MMarks[1][2]", "MMarks[1][3]"], "distractors": ["Maximum cost for strategy 1 is {Cmax[0]}. The minimum max cost is {Lminmax}.", "Maximum cost for strategy 2 is {Cmax[2]}. The minimum max cost is {Lminmax}.", "Maximum cost for strategy 3 is {Cmax[2]}. The minimum max cost is {Lminmax}.", "Maximum cost for strategy 4 is {Cmax[3]}. The minimum max cost is {Lminmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Savage criterion, which strategies could be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[2][0]", "MMarks[2][1]", "MMarks[2][2]", "MMarks[2][3]"], "distractors": ["Maximum regret for strategy 1 is {Rmax[0]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 2 is {Rmax[1]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 3 is {Rmax[2]}. The minimum maximum regret is {Rminmax}.", "Maximum regret for strategy 4 is {Rmax[3]}. The minimum maximum regret is {Rminmax}."]}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "By the Hurwicz criterion with coefficient of optimism $\\alpha = \\var{alpha}$, which strategy would be chosen?
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["strategy 1", "strategy 2", "strategy 3", "strategy 4"], "matrix": ["MMarks[3][0]", "MMarks[3][1]", "MMarks[3][2]", "MMarks[3][3]"], "distractors": ["Hurwicz score for strategy 1 is {Hscore[0]}. The best score is {Hbest}.", "Hurwicz score for strategy 2 is {Hscore[1]}. The best score is {Hbest}.", "Hurwicz score for strategy 3 is {Hscore[2]}. The best score is {Hbest}.", "Hurwicz score for strategy 4 is {Hscore[3]}. The best score is {Hbest}."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Decision making under uncertainty (Investment Banker)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_jtnt3ZK.png", "/srv/numbas/media/question-resources/image_jtnt3ZK.png"], ["question-resources/image_YeZFAo0.png", "/srv/numbas/media/question-resources/image_YeZFAo0.png"], ["question-resources/image_OU9Lgsp.png", "/srv/numbas/media/question-resources/image_OU9Lgsp.png"], ["question-resources/image_unfUEiZ.png", "/srv/numbas/media/question-resources/image_unfUEiZ.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Corry", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/8910/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "An investment banker will choose 1 of 3 proposed investment strategies. The banker has modelled 4 possible scenarios in terms of global economic conditions that will determine the likely return for each of these investment strategies. The probability of each of the scenarios occuring is unknown. The following matrix $L$ represents the anticipated percentage returns with $L_{ij}$ giving the return for strategy $i \\in \\{1,2,3\\}$ under scenario $j \\in \\{1,2,3,4\\}$.
\n$L = \\var{L}$
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\n$L = \\var{L}$
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