In a certain probability problem, we have 11 variables: A, B 1 , B 2 , ..., B 10
ID: 3598678 • Letter: I
Question
In a certain probability problem, we have 11 variables: A, B1, B2, ..., B10.
Variable A has 5 values.
Each of variables B1, ..., B10 has 7 possible values. Each Bi is conditionally independent of all other 9 Bjvariables (with j != i) given A.
Based on these facts:
Part a: How many numbers do you need to store in the joint distribution table of these 11 variables?
Part b: What is the most space-efficient way (in terms of how many numbers you need to store) representation for the joint probability distribution of these 11 variables? How many numbers do you need to store in your solution? Your answer should work with any variables satisfying the assumptions stated above.
Explanation / Answer
Part a)
The B variables are conditionaly independent and each can have aby of 7 values, so it will give 710 deifferent values.
The variable A can have 5 different values, So total 5*710 many numbers is needed to store in joint distribution table.
Part b)
The variable A can have 5 possible values, So we have to store these 5 value. we cannot reduce this. Corresponding to 5 possible value of A we have 710 many possible values for B varaible. But we need to store only one table for 710 values.
So in space-efficient way we need to store 5+710 many numbers.
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