【#官方解释西安出现蓝太阳#】4月23日早晨，陕西西安出现浮尘天气，天空昏黄、太阳呈偏蓝的苍白色，能见度下降，给交通出行带来不利影响。

中国天气首席气象分析师“Walle胡啸”介绍，由于沙尘里的颗粒物散射和吸收了波长更长的红光，导致红光减少，所以太阳看起来是蓝色的。（据中国天气）#西安[地点]#

ECE6913 Introduction to Machine
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Problem 1 (90 points)

WallE is looking for Eve using his cameras but can’t find Eve. WallE has small circuits for performing the junction-tree algorithm. Help him out by designing a junction-tree from the graph below which WallE has in his mind for Eve.



Problem 2 (60 points)

Consider the Bayesian network below with binary variables x1, x2, . . . , x5.



Write out the factorization of the probability distribution p(x1, ..., x7) implied by this directed graph. (10 points) Then, using the Bayes ball algorithm, indicate for each statement below if it is True or False and justify your answers (50 points)

• x2 and x6 are independent.

• x2 and x6 are conditionally independent given x1, x3, and x5.

• x1 and x7 are conditionally independent given x5.

• x5 and x3 are conditionally independent given x1 and x2.

• x5 and x6 are conditionally independent given x1, x2, and x4.

• x5 and x6 are conditionally independent given x4.

• x5 and x6 are conditionally independent given x1.

• x2 and x6 are conditionally independent given x3 and x5.

• x1 and x7 are independent.

• x1 and x7 are conditionally independent given x4.

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