Consider a Decision Situation with Four Possible States of Nature

question 1

Essay

Consider a decision situation with four possible states of nature: s1, s2, s3, and s4. The prior probabilities are P(s1) = 0.35, P(s2) = 0.15, P(s3) = 0.20, P(s4) = 0.30. The conditional probabilities are P(C|s1) = 0.2, P(C|s2) = 0.09, P(C|s3) = 0.15, and P(C|s4) = 0.20. Find the revised (posterior) probabilities P(s1|C), P(s2|C), P(s3|C), and P(s4|C).

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Definitions:

Sample

A subset of individuals or objects taken from the population of interest, used for statistical analysis.

Simple Random Sampling

A sampling method where each member of a population has an equal probability of being selected into the sample.

Sample Mean

The sample mean is the average value of a sample of data, calculated by summing all data points and dividing by the number of points.

Random Variable

A variable whose values depend on outcomes of a probabilistic phenomenon.