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Assume two Classmates A and B are assigned an extra group project. Each student can choose to Shirk or Work. If one or more players chooses Work, the project is completed and provides each with extra credit valued at 4 payoff units each. The cost of completing the project is that 6 total units of effort (measured in payoff units) is divided equally among all players who choose to Work and this is subtracted from their payoff. If both shirk, they do not have to expend any effort but the project is not completed, giving each a payoff of 0. The teacher can only tell whether the project is completed and not which student contributed to it.
(A.) Create a payoff matrix for this game assuming students choose to slack or work simultaneously.
(B.) Find the Nash equilibrium and explain why the result you found is a Nash equilibrium.
(C.) What type of game does this resemble? Explain how the outcome in b) can change
Suppose you are planning entering a market serviced through a monopolist. You currently receive $0 economic profits, while monopolist receives $5.
A famous hypnotist performs to a crowd of 350 students and 180 non-students. The hypnotist knows from previous experience that one half of the students and two third on the non-students are hypnotizable. What is the probability that a randomly cho..
After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not)..
Suppose you have been offered chance to participate in a Treasure Hunt game whose rules are as follows. There are 3-colored boxes: red, green and yellow.
You are given the information that P(A) = 0.30 and P(B) = 0.40 (a) Do you have enough information to compute P(A or B)? Explain. (Events A and B are mutually b) If you know that events A and B are mutually exclusive, do you have enough information..
Test the hypothesis that random variable 30.4 31.2 30.8 29.9 30.4 30.7 29.9 30.1 come from a normal distribution with mean 30.5. The standard deviation of the measurements is known to be 0.1
A certain tennis player makes a successful first serve 75% of the time. Assume that each serve is independent of the others. If she serves 5 times, what's the probability she gets:
It provides a range of values, any of which is a good guess at the possible value of the sample mean.
A 5-card poker hand is said to be a full house if it consists of 3 cards of the same denomination and two other cards of the same denomination(of course,different from the first denomination). How many hands of full house are possible?
Assuming the life length of batteries is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, 0.0234 would be a legitimate entry.
Elly's Hotdog Emporium is famous for its chilidogs. Elly's latest sales indicate that 30% of the customers order their chilidogs with hot peppers. Suppose 15 customers are selected at random. What is the probability that between two and six people..
National polls are often conducted by asking the opinions of a few thousand adults nationwide and using them to infer the opinions of all adults in the nation. Explain who is in the sample and who is in the population for such polls. Please use a ..
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