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Bayes Net Reasoning (4%) [4%] Consider the following Covid network P(C) +C 0.1 Covid -C 0.9 Suffering C S P(S|C) +C +S 0.8 +C -S 0.2 -c +S 0.75 -S 0.25 C A P(A|C) +C +a 0.95 Antigen +c -a 0.05 Test -C +a 0.25 -c -a 0.75 PCR C S P P(P|C,S) +C +S +p 0.9 +C +s -P 0.1 +C -S +p 0.7 +C -S -P 0.3 -€ +s +p 0.55 -c +S -P 0.45 -C -S +P 0.15 -C -S -P 0.85 Answer the following questions (up to 3 decimal points): a) (1%) - What is the probability of having Covid and getting a positive PCT test? P(+c, +p)= Hint: Please review variable elimination slides as there is a variable here that needs to be eliminated (i.e., summed out) to calculate the above probability b) (1%) - What is the probability of not having Covid and getting a positive PCR test? P(-c, +p)= Same hint as above applies c) (1%) - Conditional probability review - What is the probability of having Covid given that the PCR test has been positive P(+c|+p) = Hint: Conditional probability slides and formula review d) (1%) - Bayes theorem review: What is the probability of having Covid given that the Antigen test has been positive? P(+c+a)=

Bayes Net Reasoning (4%) [4%] Consider the following Covid network P(C) +C 0.1 Covid -C 0.9 Suffering C S P(S|C) +C +S 0.8 +C -S 0.2 -c +S 0.75 -S 0.25 C A P(A|C) +C +a 0.95 Antigen +c -a 0.05 Test -C +a 0.25 -c -a 0.75 PCR C S P P(P|C,S) +C +S +p 0.9 +C +s -P 0.1 +C -S +p 0.7 +C -S -P 0.3 -€ +s +p 0.55 -c +S -P 0.45 -C -S +P 0.15 -C -S -P 0.85 Answer the following questions (up to 3 decimal points): a) (1%) - What is the probability of having Covid and getting a positive PCT test? P(+c, +p)= Hint: Please review variable elimination slides as there is a variable here that needs to be eliminated (i.e., summed out) to calculate the above probability b) (1%) - What is the probability of not having Covid and getting a positive PCR test? P(-c, +p)= Same hint as above applies c) (1%) - Conditional probability review - What is the probability of having Covid given that the PCR test has been positive P(+c|+p) = Hint: Conditional probability slides and formula review d) (1%) - Bayes theorem review: What is the probability of having Covid given that the Antigen test has been positive? P(+c+a)=

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Bayes Net Reasoning (4%) [4%] Consider the following Covid network P(C) +C 0.1 Covid -C 0.9 Suffering C S P(S|C) +C +S 0.8 +C -S 0.2 -c +S 0.75 -S 0.25 C A P(A|C) +C +a 0.95 Antigen +c -a 0.05 Test -C +a 0.25 -c -a 0.75 PCR C S P P(P|C,S) +C +S +p 0.9 +C +s -P 0.1 +C -S +p 0.7 +C -S -P 0.3 -€ +s +p 0.55 -c +S -P 0.45 -C -S +P 0.15 -C -S -P 0.85 Answer the following questions (up to 3 decimal points): a) (1%) - What is the probability of having Covid and getting a positive PCT test? P(+c, +p)= Hint: Please review variable elimination slides as there is a variable here that needs to be eliminated (i.e., summed out) to calculate the above probability b) (1%) - What is the probability of not having Covid and getting a positive PCR test? P(-c, +p)= Same hint as above applies c) (1%) - Conditional probability review - What is the probability of having Covid given that the PCR test has been positive P(+c|+p) = Hint: Conditional probability slides and formula review d) (1%) - Bayes theorem review: What is the probability of having Covid given that the Antigen test has been positive? P(+c+a)=
Transcribed Image Text:Bayes Net Reasoning (4%) [4%] Consider the following Covid network P(C) +C 0.1 Covid -C 0.9 Suffering C S P(S|C) +C +S 0.8 +C -S 0.2 -c +S 0.75 -S 0.25 C A P(A|C) +C +a 0.95 Antigen +c -a 0.05 Test -C +a 0.25 -c -a 0.75 PCR C S P P(P|C,S) +C +S +p 0.9 +C +s -P 0.1 +C -S +p 0.7 +C -S -P 0.3 -€ +s +p 0.55 -c +S -P 0.45 -C -S +P 0.15 -C -S -P 0.85 Answer the following questions (up to 3 decimal points): a) (1%) - What is the probability of having Covid and getting a positive PCT test? P(+c, +p)= Hint: Please review variable elimination slides as there is a variable here that needs to be eliminated (i.e., summed out) to calculate the above probability b) (1%) - What is the probability of not having Covid and getting a positive PCR test? P(-c, +p)= Same hint as above applies c) (1%) - Conditional probability review - What is the probability of having Covid given that the PCR test has been positive P(+c|+p) = Hint: Conditional probability slides and formula review d) (1%) - Bayes theorem review: What is the probability of having Covid given that the Antigen test has been positive? P(+c+a)=
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