Question

In a certain probability problem, we have 11 variables: A, B₁, B₂, ..., B₁₀.

• Variable A has 6 values.
• Each of variables B₁, ..., B₁₀ have 5 possible values. Each B_i is conditionally indepedent of all other 9 B_jvariables (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.

Answer 1

Part A

Here as we can See

B is Conditional independent and each have values 5 values so it has 5^10 different values

And while comming to the A we have only 6 Values

now the total we can Store is

6*(5^10)

is our required answers

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Part B

As we can see

A has only 6 values

B can have 5^10 values

here we have 6+(5^10) possible ways

this is our required answer

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