Answer the following questions and provide a brief explanation: How many values does it take to...

Answer the following questions and provide a brief explanation:

How many values does it take to represent a joint distribution p(x, y) of 4 boolean variables?
How many of these values can be chosen independently?
What are the answers for the above question if we know that x and y are independent?

Expert Solution

1. 2^n values it take... That is for joint distribution f(x,y) 4 boolean variables it requires 2^4 = 16 values.

Because, 1 variable should be compared to all other variables so that 4 to 4 so it will be 16 values... Example in the image below :

2. The variables whose joint Cumulative Distribution Function is equal to product of marginal Cumulative Distribution Function are taken as independent variables.

Because, Jointly-distributed random variables X and Y are independent if their joint Cumulative Distribution Function is the product of the marginal Cumulative Distribution Function :
F(X, Y ) = FX(x)FY (y).

3. x, y are independent if theirs Cumulative Distribution Function = product of marginal Cumulative Distribution Function..

And

There are 16 values required for 4 boolean variables.

venereology answered 4 months ago

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