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VE492Homework6
Question 1: Probability, Part I
Below is a table listing the probabilities of three binary random variables. Please writedown the correct values for each marginal or conditional probability expression. Andeach value for one row. (3 significant figures)
Sample Answer:
0.160
0.200
0.333 …
0 0 0 0.060
1 0 0 0.020
0 1 0 0.280
1 1 0 0.080
0 0 1 0.100
1 0 1 0.200
0 1 1 0.140
1 1 1 0.120
Expression:
Question 2: Probability, Part II
You are given the prior distribution P(X), and two conditional distributions P(Y|X)
and P(Z|Y) as below (you are also given the fact that Z is independent fromXgivenY). All variables are binary variables. Compute the table of their joint distributionbased on the chain rule. And write your answers for each blank in one rowwiththe same format in Question 1. 0 0.300
1 0.700
0 0 0.500
1 0 0.500
0 1 0.900
1 1 0.100
Table 1
0 0
1 0
0 1
1 1
Table 2
0 0 0 0.030
1 0 0
0 1 0 0.060
1 1 0 0.028
0 0 1 0.120
1 0 1
0 1 1
1 1 1
0 0 0.200
1 0 0.800
0 1 0.400
1 1 0.600
Question 3: Probability, Part III
For the following four subparts, you are given three joint probability distributiontables. For each distribution, please identify if the given independence/conditional
independence assumption is true or false (write 'true' or 'false'). For your
convenience, we have also provided some marginal and conditional probabilitydistribution tables that could assist you in solving this problem. Please write your answer for each subpart in one row. 1) Assumption: is independent from .
2) Assumption: is independent from .
3) Assumption: is independent from given .
4) Assumption: is independent from given .