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The joint probabilities are summarized in the table below and we found P(I) = 0.09. Compute the posterior probabilities, rounding the results to four decimal places. Prior Probabilities P(s;) Posterior Probabilities P(s; II) States of Nature $1 $2 $3 0.5 0.4 0.1 Conditional Probabilities P(I|s;) 0.1 0.05 0.2 Joint Probabilities P(Ins;) 0.05 0.02 0.02 P(S₁|I) = = P(Ins₁) P(I) 0.05 0.09

The joint probabilities are summarized in the table below and we found P(I) = 0.09. Compute the posterior probabilities, rounding the results to four decimal places. Prior Probabilities P(s;) Posterior Probabilities P(s; II) States of Nature $1 $2 $3 0.5 0.4 0.1 Conditional Probabilities P(I|s;) 0.1 0.05 0.2 Joint Probabilities P(Ins;) 0.05 0.02 0.02 P(S₁|I) = = P(Ins₁) P(I) 0.05 0.09

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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The joint probabilities are summarized in the table below and we found P(1) States of Nature S1 S2 $3 Prior Probabilities P(s;) 0.5 0.4 0.1 = 0.09. Compute the posterior probabilities, rounding the results to four decimal places. Conditional Probabilities P(I\s;) 0.1 0.05 0.2 Joint Probabilities P(Ins;) 0.05 0.02 0.02 Posterior Probabilities P(s; I) P(S₁|I) = P(Ins₁) P(I) 0.05 0.09
Transcribed Image Text:The joint probabilities are summarized in the table below and we found P(1) States of Nature S1 S2 $3 Prior Probabilities P(s;) 0.5 0.4 0.1 = 0.09. Compute the posterior probabilities, rounding the results to four decimal places. Conditional Probabilities P(I\s;) 0.1 0.05 0.2 Joint Probabilities P(Ins;) 0.05 0.02 0.02 Posterior Probabilities P(s; I) P(S₁|I) = P(Ins₁) P(I) 0.05 0.09
Suppose that you are given a decision situation with three possible states of nature: S₁, S₂, and s3. The prior probabilities are P(s₁) = 0.5, P(s₂) = 0.4, and P(53) = 0.1. With sample information I, P(I|s₁) = 0.1, P(I|s₂) = 0.05, and P(I|s3) = 0.2. Compute the revised or posterior probabilities: P(S₁|I), P(S₂|I), and P(s3|I). Step 1 Posterior probabilities are conditional probabilities based on the outcome of the sample information. These can be computed by developing a table using the following process. 1. Enter the states of nature in the first column, the prior probabilities for the states of nature, P(I|s;), in the second column and the conditional probabilities in the third column. 2. In column 4 compute the joint probabilities by multiplying the prior probability values in column 2 by the corresponding conditional probabilities in column 3. 3. Sum the joint probabilities in column 4 to obtain the probability of the sample information I, P(I). 4. In column 5, divide each joint probability in column 4 by P(I) to obtain the posterior probabilities, P(s¡|1). The prior probabilities are given to be P(s₁) = 0.5, P(s₂) = 0.4, and P(S3) = 0.1. The conditional probabilities given each state of nature are P(I|s₁) = 0.1, P(I|s₂) = 0.05, and P(I|s3) 0.2. Use the given prior and conditional probabilities to compute the joint probabilities. States of Nature Prior Probabilities P(s;) Conditional Probabilities P(I|s;) S1 52 = $3 P(S₁) = 0.5 P(S₂) = 0.4 P(S3) = 0.1 The sum of the Joint Probabilities column gives P(I) = .09 0.09 P(I|s₁) = 0.1 P(I|S₂) = 0.05 P(I|S3) = = 0.2 Joint Probabilities P(I n s;) P(In S₁) = P(S₁)P(I|S₁) 0.5 (0.1) .05 = = .02 .02 0.02 0.02 0.05
Transcribed Image Text:Suppose that you are given a decision situation with three possible states of nature: S₁, S₂, and s3. The prior probabilities are P(s₁) = 0.5, P(s₂) = 0.4, and P(53) = 0.1. With sample information I, P(I|s₁) = 0.1, P(I|s₂) = 0.05, and P(I|s3) = 0.2. Compute the revised or posterior probabilities: P(S₁|I), P(S₂|I), and P(s3|I). Step 1 Posterior probabilities are conditional probabilities based on the outcome of the sample information. These can be computed by developing a table using the following process. 1. Enter the states of nature in the first column, the prior probabilities for the states of nature, P(I|s;), in the second column and the conditional probabilities in the third column. 2. In column 4 compute the joint probabilities by multiplying the prior probability values in column 2 by the corresponding conditional probabilities in column 3. 3. Sum the joint probabilities in column 4 to obtain the probability of the sample information I, P(I). 4. In column 5, divide each joint probability in column 4 by P(I) to obtain the posterior probabilities, P(s¡|1). The prior probabilities are given to be P(s₁) = 0.5, P(s₂) = 0.4, and P(S3) = 0.1. The conditional probabilities given each state of nature are P(I|s₁) = 0.1, P(I|s₂) = 0.05, and P(I|s3) 0.2. Use the given prior and conditional probabilities to compute the joint probabilities. States of Nature Prior Probabilities P(s;) Conditional Probabilities P(I|s;) S1 52 = $3 P(S₁) = 0.5 P(S₂) = 0.4 P(S3) = 0.1 The sum of the Joint Probabilities column gives P(I) = .09 0.09 P(I|s₁) = 0.1 P(I|S₂) = 0.05 P(I|S3) = = 0.2 Joint Probabilities P(I n s;) P(In S₁) = P(S₁)P(I|S₁) 0.5 (0.1) .05 = = .02 .02 0.02 0.02 0.05
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