step 2 please. Thank you. The joint probabilities are summarized in the table below and we found P(1)States ofNatureS1S2$3Prior ProbabilitiesP(s;)0.50.40.1=0.09. Compute the posterior probabilities, rounding the results to four decimal places.Conditional ProbabilitiesP(I\s;)0.10.050.2Joint ProbabilitiesP(Ins;)0.050.020.02Posterior ProbabilitiesP(s; I)P(S₁|I)=P(Ins₁)P(I)0.050.09 Suppose that you are given a decision situation with three possible states of nature: S₁, S₂, and s3. The prior probabilities areP(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 1Posterior probabilities are conditional probabilities based on the outcome of the sample information. These can be computed by developing a table using the followingprocess.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 conditionalprobabilities 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 incolumn 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 areP(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;)S152=$3P(S₁) = 0.5P(S₂) = 0.4P(S3) = 0.1The sum of the Joint Probabilities column gives P(I) = .090.09P(I|s₁) = 0.1P(I|S₂) = 0.05P(I|S3) == 0.2Joint Probabilities P(I n s;)P(In S₁) = P(S₁)P(I|S₁)0.5 (0.1).05==.02.020.020.020.05

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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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