The prior probabilities for events A1, A2, and A3 are P(A1) = 0.10, P(A2) = 0.60, and P(A3) = 0.30. The conditional probabilities of event B given A1, A2, and A3 are P(B|A1) = 0.50, P(B|A2) = 0.40, and Р(B Аз) 3D 0.20. Round your answers to two decimal places. a. Compute P(B n A1) , P(BN A2), and P(BN A3). P(BN A1) = 0.05 P(BN A2) = 0.24 P(BN A3) = 0.06 b. Apply Bayes' theorem, to compute the posterior probability P(A2|B). P(A; N B ) = P(A;)P(B|A;) P(A1)P(B|A1 )+ 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). P(A; N B) Events P(A;) P(B|A;) P(A;|B) A1 A2 Аз Total:
The prior probabilities for events A1, A2, and A3 are P(A1) = 0.10, P(A2) = 0.60, and P(A3) = 0.30. The conditional probabilities of event B given A1, A2, and A3 are P(B|A1) = 0.50, P(B|A2) = 0.40, and Р(B Аз) 3D 0.20. Round your answers to two decimal places. a. Compute P(B n A1) , P(BN A2), and P(BN A3). P(BN A1) = 0.05 P(BN A2) = 0.24 P(BN A3) = 0.06 b. Apply Bayes' theorem, to compute the posterior probability P(A2|B). P(A; N B ) = P(A;)P(B|A;) P(A1)P(B|A1 )+ 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). P(A; N B) Events P(A;) P(B|A;) P(A;|B) A1 A2 Аз Total:
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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Transcribed Image Text:The prior probabilities for events A1, A2, and A3 are P(A1) = 0.10, P(A2) = 0.60, and P(A3) = 0.30.
The conditional probabilities of event B given A1, A2, and A3 are P(B|A1) = 0.50, P(B|A2) = 0.40, and
Р(B Аз) 3D 0.20.
Round your answers to two decimal places.
a. Compute P(B n A1) , P(BN A2), and P(BN A3).
P(BN A1) =
0.05
P(BN A2) =
0.24
P(BN A3) =
0.06
b. Apply Bayes' theorem, to compute the posterior probability P(A2|B).
P(A; N B ) =
P(A;)P(B|A;)
P(A1)P(B|A1 )+ 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).
P(A; N B)
Events
P(A;)
P(B|A;)
P(A;|B)
A1
A2
A3
Total:
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