5. Shift-in-charge Nazar Al Rushdy: Nazar is pessimistic about the market price. What is your guidance for Nazar? The decision to employ decision trees in crucial situations has been taken by Salem Al Harthi, the plant manager. The table below presents data on demand for a duration of 6 hours along with their respective probabilities. The first row of the table provides the probability of demand for the initial three hours when a leak occurs, denoted in parentheses. Subsequently, the following three rows indicate the probabilities of high, medium, and low demand for the succeeding three hours. To illustrate, if the initial 3-hour market price was low, the probabilities of high demand, medium demand, and low demand in the next three hours are 0.2, 0.3, and 0.5, respectively. Market price High Market price Medium Initial 3-hrs (0.2) Initial 3-hrs (0.5) Market price Low Initial 3-hrs (0.3) High demand (next (0.5) (0.4) (0.2) 3 hrs) Medium demand (0.3) (0.2) (0.3) (next 3 hours) Low demand (next (0.2) (0.4) (0.5) 3 hours) Discussion Question 6. Make a decision tree and suggest what decision to make: repair HRSG immediately or delay it for the next shift.

Suppose 1,250 raffle tickets are being sold for $5 each. One ticket will be chosen to receive a cash prize of $2,500, and three tickets will be chosen to recelve cash prizes of $500. Let x be the amount of money won/lost by purchasing one raffle ticket. Find the expected value for . (Round your answer to the nearest penny. Do not include as sign in your answer. Your answer may be positive or negative.)

a and b please

Consider the following interaction between a student and a company. The student is either serious or lazy with probabilities 1/3 and 2/3 respectively. The student knows if they are serious or not, but the company does not. Initially, the student decides whether to revise for exams or not. Revising has a cost of 1 for a serious student and 3 for a lazy one. The company observes the student's exam result (that is, whether they have made the effort to revise), and based on this, offers a salary of 3 (for a serious student) or 1 (for a lazy student). The student learns of the proposed salary and can then either accept (and earn the salary) or refuse (and earn O). They also lose the revision effort if they worked. The company's gain is equal to the student's productivity (4 if they are serious, 2 if not) minus the salary if the student accepts the offer, and O otherwise. 1. Represent the game in extensive form. 2. Show that the game has a unique perfect Bayesian Equilibrium, and provide the…