You Are Given the Opportunity to Guess Whether a Coin

question 5

Essay

You are given the opportunity to guess whether a coin is fair or two-headed,where the prior probabilities are 0.5 for each of these possibilities.If you are correct,you win $5; otherwise,you lose $5.You are also given the option of seeing a demonstration flip of the coin before making your guess.You wish to use Bayes' decision rule to maximize expected profit.(a)Develop a decision analysis formulation of this problem by identifying the decision alternatives,states of nature,and payoff table.(b)What is the optimal decision alternative,given that you decline the option of seeing a demonstration flip? (c)Find EVPI.d)Calculate the posterior distribution if the demonstration flip is a tail.Do the same if the flip is a head.
(e)Determine your optimal policy.(f)Now suppose that you must pay to see the demonstration flip.What is the most that you should be willing to pay? (g)Draw the complete decision tree for this problem and label all the branches.Write the cash flow incurred at each branch or terminal node underneath that branch or node.Write the probability associated with each branch emanating from an event node above that branch.At each decision node,insert a 1 or 2 inside the node to indicate whether the optimal decision there is to choose the upper branch (indicated by a 1)or to choose the lower branch (indicated by a 2).Next to each decision node and event node,write the expected payoff at that node if the optimal policy is being followed.

---

Definitions:

Coefficient

A numerical value or constant that defines the relationship between two variables in mathematical equations or models, indicating how one variable changes in relation to another.

Repetitions

The action of repeating something, such as an exercise or task, multiple times to improve proficiency, strength, or conditioning.

Time Per Unit

The average amount of time required to produce one unit of a product or service.

Learning Curves

A concept that illustrates how the time taken to complete a task decreases with an increasing number of trials or experiences, due to the increase in efficiency and skill.