You Are Given a Decision Situation with Three Possible States $\mid$

question 39

Essay

You are given a decision situation with three possible states of nature S₁, S₂, and S₃. The prior probabilities of the three states are 0.20, 0.45, and 0.35. With sample information I, you are provided with the following information.
P(I₁ $\mid$ S₁) = 0.85
P(I₁ $\mid$ ₂) = 0.70
P(I₁ $\mid$ S₃) = 0.40
a.Compute P(I).
b.Compute the revised probabilities of P(S₁ $\mid$ I), P(S₂ $\mid$ I), and P(S₃ $\mid$ I).

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Definitions:

Reorder Interval

The time between placing orders for inventory replenishment to ensure stock levels remain adequate.

Inventory Cost

Expenses related to holding and managing inventory, including storage, insurance, taxes, and costs associated with unsold or obsolete items.

Customer Service Level

A measurement of the ability of a company to provide services to its customers within a specified time frame and quality standard.

Holding Cost

The expenses associated with storing unsold goods, including warehousing, insurance, and spoilage costs.