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日期：2024-04-16 09:24

2023-24 Second Semester AI3043 Bayesian Networks

Assignment 2 Exact Inference: Variable Elimination

Due Date: 17/Apr/2024(Wed), before 11:59am, submitted to iSpace

Consider the following Bayesian networks:

• R: it is raining or not, with binary values r: it is raining and r

c

: it is not raining. val(R) = {r, rc}

• L: there are juicy leaves or not, val(L) = {l, lc}

• Q: the quokkas are happy or unhappy, val(Q) = {q, qc}

• T: there are lots of tourist or not many, val(T) = {t, tc}

• S: people are taking lots of quokka selfies, or not. val(R) = {s, sc}

Figure 1: Bayesian network

1. Write the chain rule for the joint distribution P (R, L, Q, T, S)

P (R, L, Q, T, S) = P (R) P (L | R) P (Q | R, L) P (T | R, L, Q) P (S | R, L, Q, T)

Note: You must use VE (variable elimination) method to solve these questions below!

2. What is the probability that there are many tourists?

3. What is the probability that the quokkas are happy, given there are lots of quokka selfies being taken and it

is not raining.

4. Calculate P (r | l

c

, s), what does the this probability stand for?

5. Calculate P (l | q, t, s)

1