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# A b we have to find a and b

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hour. Let N(t) be the number of custoer arrivals up to time t, with hour as the unit. There are two types of soft drinks, type A and B, stored in the machine. Suppose that each time a customer deposits money, the machine dispenses one soft drink A with probability p1, or one soft drink B with probability p2. We have p1 + p2 = 1, p1 > 0, p2 > 0. Let X(t) be the number of type A soft drinks dispensed up to time t; and Y (t) be the number of type B soft drinks dispensed up to time t.
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subgame perfect Nash equilibrium? Question 3: In which situations should we need the mixed extension of a game? Question 4: Find, if any, all Nash equilibria of the following famous matrix game: L R U (2,0) (3,3) D (3,4) (1,2) Question 5: What is the difference between a separating equilibrium and a pooling equilibrium in Bayesian games? Question 6: Give another name for, if it exists, the intersection of the players’ best-response « functions » in a game? Question 7: assuming we only deal with pure strategies, the Prisoner’s Dilemma is a situation with: No Nash equilibrium One sub-optimal Nash equilibrium One sub-optimal dominant profile No dominant profile Question 8: If it exists, a pure Nash equilibrium is always a profile of dominant strategies: True False Question 9: All games have at least one pure strategy Nash equilibrium: True False Question 10: If a tree game has a backward induction equilibrium then it must also be a Nash equilibrium of all of its subgames: Tr 2/2 Question 11: The mixed Nash equilibrium payoffs are always strictly smaller than the pure Nash equilibrium payoffs: True False Question 12: Which of the following statements about dominant/dominated strategies is/are true? I. A dominant strategy dominates a dominated strategy in 2x2 games. II. A dominated strategy must be dominated by a dominant strategy in all games. III. A profile of dominant strategies must be a pure strategy Nash equilibrium. IV. A dominated strategy must be dominated by a dominant strategy in 2x2 games. I, II and IV only I, II and III only II and III only I and IV only I, III and IV only I and II only Question 13: A pure strategy Nash equilibrium is a special case of a mixed strategy Nash equilibrium: True False Question 14: Consider the following 2x2 matrix game: L R U (3,2) (2,4) D (-1,4) (4,3) The number of pure and mixed Nash equilibria in the above game is: 0 1 2 3 Exercise (corresponding to questions 15 to 20 below): assume a medical doctor (M) prescribes either drug A or drug B to a patient (P), who complies (C) or not (NC) with each of this treatment. In case of compliance, controlled by an authority in charge of health services quality, the physician is rewarded at a level of 1 for drug A and 2 for drug B. In case of noncompliance, the physician is « punished » at -1 level for non-compliance of the patient with drug A and at -2 level for non-compliance with drug B. As for the compliant patient, drug A should give him back 2 years of life saved and drug B, only 1 year of life saved. When noncompliant with drug A, the same patient wins 3 years of life (due to avoiding unexpected allergic shock for instance), and when non-compliant with drug B, the patient loses 3 years of life. Question 15: You will draw the corresponding matrix of the simultaneous doctor-patient game. Question 16: Find, if any, the profile(s) of dominant strategies of this game. Question 17: Find, if any, the pure strategy Nash equilibrium/equilibria of this game. Question 18: Find, if any, the mixed strategy Nash equilibrium/equilibria of this game. Questions 19 and 20: Now the doctor prescribes first, then the patient complies or not: draw the corresponding extensive-form game (= question 19) AND find the subgame perfect Nash equilibrium/equilibria (=
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inefficiencies, etc), and suggest an improved process. Open and read the Process Improvement (Final Q 1) document which describes the process steps in words and also includes a process map as a visual tool for understanding what's going on in each step. You will need to respond to the following three sub-questions: FINAL Q1: 3 Attachments are the Q1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------ I need the 3 part question answered. This is everything in the question.. Understand that there is NOTHING INCOMPLETE, I have added everything that was sent to us. ------------------------------------------------------------------------------------------------------------------------------------------------------------------ a. Of the 9 process steps in the Process Improvement (Final Q 1) document, which specific steps in that process are experiencing lean wastes and/or process cycle time issues (please note, there is more than one step experiencing issues). In your response, name the process step, and/or the transfer interface between steps, and what waste(s) or cycle time issue is involved. Be sure to use standard lean/six sigma terminology that we used in the course when referring to any of the quality concepts; e.g., transportation waste when referring to situations involving a lot of moving around from one place to another. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- b. Which of the process steps you identified in part a do you believe could benefit from process improvement and why? --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- c. What changes would you institute in the process to improve the steps you cited in part b of this question and describe how those changes improves the process. Be specific about which process step(s) your improving and thoroughly describe the improvement to that step. [Note: This question ties to what you decided was important in part b question above.] Also, when answering how you would improve a given process step, assume you have an unlimited budget and personnel resources and you can do mostly anything you want as long as it doesn't violate the laws of physics or the judicial system. Be cautious though because process improvement is designed to save time, money, and resources in doing the needed work.For example, automation is good, and also potentially expensive, so is it worth it for the improvement? - you will have to be the judge of that.
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e in the Euclidean plane. In this exercise, we will show this is not true in the Poincar´e plane. As usual, let Γ be the unit circle in R2 , and let O be the origin. Let A = (3/4, 0) and B = (0, 3/4). Consider the P-triangle △OAB. Let γ be the E-circle through O, A, and B. Show that γ contains points outside of Γ and is therefore not a P-circle. Explain why this means that the P-triangle △OAB cannot have a circumscribed circle in the Poincar´e plane.
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C D Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with ∠DAB = x, and ∠ABC = 90◦ , and AD = BC. Say the perpendicular bisector to DC meets the perpendicular bisector to AB at P. Then P A = P B and P C = P D. So the triangles P AD and P BC have equal sides and are congruent. Thus ∠P AD = ∠P BC. But P AB is isosceles, hence ∠P AB = ∠P BA. Subtracting, gives x = ∠P AD − ∠P AB = ∠P BC − ∠P BA = 90◦ . This is a preposterous conclusion – just where is the mistake in the “proof” and why does the argument break down there?
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics