Consider the Following Problem with Four States of Nature,three Decision

question 27

Essay

Consider the following problem with four states of nature,three decision alternatives,and the following payoff table (in $'s): $$\begin{array} { l | c c c c } & s _ { 1 } & s _ { 2 } & s _ { 3 } & s _ { 4 } \\\hline d _ { 1 } & 200 & 2600 & - 1400 & 200 \\d _ { 2 } & 0 & 200 & - 200 & 200 \\d _ { 3 } & - 200 & 400 & 0 & 200\end{array}$$ The indifference probabilities for three individuals are: $$\begin{array} { r c c c } \text { Payoff } & \text { Person 1 } & \text { Person 2 } & \text { Person 3 } \\\hline\$ 2600 & 1.00 & 1.00 & 1.00 \\\$ 400 & .40 & .45 & .55 \\\$ 200 & .35 & .40 & .50 \\\$ 0 & .30 & .35 & .45 \\- \$ 200 & .25 & .30 & .40 \\- \$ 1400 & 0 & 0 & 0\end{array}$$
a. Classify each person as a risk avoider, risk taker, or risk neutral.
b. For the payoff of $400, what is the premium the risk avoider will pay to avoid risk? What is the premium the risk taker will pay to have the opportunity of the high payoff?
c. Suppose each state is equally likely. What are the optimal decisions for each of these three people?

Relate the normal probability distribution's applicability to the binomial distribution through specific conditions.

Understand the effects of sample size and confidence levels on the margin of error and confidence intervals for population means and proportions.

Grasp the concept of level of significance (α) and its relation to confidence levels.

Comprehend how sample size influences the degrees of freedom in a t-distribution.

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Definitions:

Working Capital Accounts

Accounts related to the short-term financial operations of a business, such as cash, inventory, and accounts payable and receivable.

Accounts Receivable

Funds that customers owe to a company for products or services provided but not yet compensated for.

Inventory Balances

Refers to the total value or quantity of all stock items held by a company at any given time, crucial for managing supply chain and sales.

Accounts Receivable

Accounts receivable is the balance of money due to a firm for goods delivered or services provided but not yet paid for by customers.