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The prior probabilities for events A₁, A2, and A3 are P(A₁) = 0.20, P(A₂) = 0.30, and P(A3) = 0.50. The conditional probabilities of event B given A₁, A2, and A3 are P(B | A₁) = 0.50, P(B | A₂) = 0.30, and P(B | A3) = 0.40. (Assume that A₁, A₂, and A3 are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B n A₁), P(B n A₂), and P(B n A3). P(B n A₁) = P(B n A₂) = P(B n A3) = P(A₁)P(BIA) to compute the posterior probability P(A₂ | B). (Round your answer to two decimal (b) Apply Bayes' theorem, P(A, | B) = places.) P(A₁)P(B|A₂) + P(A₂)P(B | A₂) + ··· + P(A)P(B | A„)´ (c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ | B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A₁) P(B|A₂) P(A₁n B) P(A₁ | B) A₁ 0.20 0.50 A₂ 0.30 0.30 0.50 0.40 1.00 1.00 A3

The prior probabilities for events A₁, A2, and A3 are P(A₁) = 0.20, P(A₂) = 0.30, and P(A3) = 0.50. The conditional probabilities of event B given A₁, A2, and A3 are P(B | A₁) = 0.50, P(B | A₂) = 0.30, and P(B | A3) = 0.40. (Assume that A₁, A₂, and A3 are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B n A₁), P(B n A₂), and P(B n A3). P(B n A₁) = P(B n A₂) = P(B n A3) = P(A₁)P(BIA) to compute the posterior probability P(A₂ | B). (Round your answer to two decimal (b) Apply Bayes' theorem, P(A, | B) = places.) P(A₁)P(B|A₂) + P(A₂)P(B | A₂) + ··· + P(A)P(B | A„)´ (c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ | B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A₁) P(B|A₂) P(A₁n B) P(A₁ | B) A₁ 0.20 0.50 A₂ 0.30 0.30 0.50 0.40 1.00 1.00 A3

MATLAB: An Introduction with Applications
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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The prior probabilities for events A₁, A2, and A3 are P(A₁) = 0.20, P(A₂) = 0.30, and P(A3) = 0.50. The conditional probabilities of event B given A₁, A₂, and A3 are P(B | A₁) = 0.50, P(B | A₂) = 0.30, and P(B | A3) = 0.40. (Assume that A₁, A₂, and A3 are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B ʼn A₁), P(B n A₂), and P(B n A3). P(B n A₁) P(B n A₂) = P(B n A3) = P(A₁)P(B | A₁) (b) Apply Bayes' theorem, P(A¡ | B) = 7 to compute the posterior probability P(A₂ | B). (Round your answer to two decimal P(A₁)P(B | A₁) + P(A₂)P(B | A₂) + + P(An)P(B | An)' places.) (c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ | B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A₁) | P(B | A;) P(A¡n B) P(A¡ | B) A₁ 0.20 0.50 A₂ 0.30 0.30 A3 0.50 0.40 1.00 1.00 0.00
Transcribed Image Text:The prior probabilities for events A₁, A2, and A3 are P(A₁) = 0.20, P(A₂) = 0.30, and P(A3) = 0.50. The conditional probabilities of event B given A₁, A₂, and A3 are P(B | A₁) = 0.50, P(B | A₂) = 0.30, and P(B | A3) = 0.40. (Assume that A₁, A₂, and A3 are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B ʼn A₁), P(B n A₂), and P(B n A3). P(B n A₁) P(B n A₂) = P(B n A3) = P(A₁)P(B | A₁) (b) Apply Bayes' theorem, P(A¡ | B) = 7 to compute the posterior probability P(A₂ | B). (Round your answer to two decimal P(A₁)P(B | A₁) + P(A₂)P(B | A₂) + + P(An)P(B | An)' places.) (c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ | B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A₁) | P(B | A;) P(A¡n B) P(A¡ | B) A₁ 0.20 0.50 A₂ 0.30 0.30 A3 0.50 0.40 1.00 1.00 0.00
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