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Burglary JohnCalls P(B) .001 Alarm A P(J) 90 f .05 Earthquake B t 1 f f f E t f 1 P(A) 95 94 29 .001 MaryCalls P(E) 002 A P(M) 1.70 f .01 Figure 1 - A typical Bayesian network, showing both the topology and the conditional probability tables (CPTS). In the CPTS, the letters B, E, A, J, and M

Burglary JohnCalls P(B) .001 Alarm A P(J) 90 f .05 Earthquake B t 1 f f f E t f 1 P(A) 95 94 29 .001 MaryCalls P(E) 002 A P(M) 1.70 f .01 Figure 1 - A typical Bayesian network, showing both the topology and the conditional probability tables (CPTS). In the CPTS, the letters B, E, A, J, and M

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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1. Consider the Bayesian network in the image attached.

If we observe Alarm = true, are Burglary and Earthquake independent? Justify
your answer explaining which of the probabilities involved satisfy the definition of
conditional independence (no need to perform the actual calculation in class).

**Figure 1:** A typical Bayesian network, showing both the topology and the conditional probability tables (CPTs). In the CPTs, the letters B, E, A, J, and M stand for Burglary, Earthquake, Alarm, JohnCalls, and MaryCalls, respectively. ### Diagram Explanation - **Nodes:** - **Burglary** and **Earthquake** are parent nodes influencing the **Alarm** node. - **Alarm** is a parent node influencing both **JohnCalls** and **MaryCalls** nodes. - **Edges:** - Directed edges from **Burglary** and **Earthquake** to **Alarm**. - Directed edges from **Alarm** to **JohnCalls** and **MaryCalls**. ### Conditional Probability Tables (CPTs) 1. **Node: Burglary (B)** - \( P(B) \) - Probability of burglary: 0.001 2. **Node: Earthquake (E)** - \( P(E) \) - Probability of earthquake: 0.002 3. **Node: Alarm (A)** - \( P(A | B, E) \) - Probability that the alarm goes off given burglary and earthquake (tt): 0.95 - Probability given burglary and no earthquake (tf): 0.94 - Probability given no burglary and earthquake (ft): 0.29 - Probability given no burglary and no earthquake (ff): 0.001 4. **Node: JohnCalls (J)** - \( P(J | A) \) - Probability that John calls given alarm (t): 0.90 - Probability given no alarm (f): 0.05 5. **Node: MaryCalls (M)** - \( P(M | A) \) - Probability that Mary calls given alarm (t): 0.70 - Probability given no alarm (f): 0.01 This Bayesian network visualizes dependencies between various events that could occur, and represents how beliefs about one event can affect beliefs about others.
Transcribed Image Text:**Figure 1:** A typical Bayesian network, showing both the topology and the conditional probability tables (CPTs). In the CPTs, the letters B, E, A, J, and M stand for Burglary, Earthquake, Alarm, JohnCalls, and MaryCalls, respectively. ### Diagram Explanation - **Nodes:** - **Burglary** and **Earthquake** are parent nodes influencing the **Alarm** node. - **Alarm** is a parent node influencing both **JohnCalls** and **MaryCalls** nodes. - **Edges:** - Directed edges from **Burglary** and **Earthquake** to **Alarm**. - Directed edges from **Alarm** to **JohnCalls** and **MaryCalls**. ### Conditional Probability Tables (CPTs) 1. **Node: Burglary (B)** - \( P(B) \) - Probability of burglary: 0.001 2. **Node: Earthquake (E)** - \( P(E) \) - Probability of earthquake: 0.002 3. **Node: Alarm (A)** - \( P(A | B, E) \) - Probability that the alarm goes off given burglary and earthquake (tt): 0.95 - Probability given burglary and no earthquake (tf): 0.94 - Probability given no burglary and earthquake (ft): 0.29 - Probability given no burglary and no earthquake (ff): 0.001 4. **Node: JohnCalls (J)** - \( P(J | A) \) - Probability that John calls given alarm (t): 0.90 - Probability given no alarm (f): 0.05 5. **Node: MaryCalls (M)** - \( P(M | A) \) - Probability that Mary calls given alarm (t): 0.70 - Probability given no alarm (f): 0.01 This Bayesian network visualizes dependencies between various events that could occur, and represents how beliefs about one event can affect beliefs about others.
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