Question

Give a joint distribution for Boolean random variables A, B, and C for each scenario. Give...

Give a joint distribution for Boolean random variables A, B, and C for each scenario. Give a brief intuitive interpretation of the variables. The notation i(x, y) means that x and y are independent.

looking for a basic understanding of independence in the context of probability.

answer should explain how these indecencies will impact probabilities.

Math   Statistics-And-Probability   
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Answer #1

Boolean random variables mean they has a logical statement either true or false. Boolean random variables are discrete random variable. The joint distribution of A, B, C (each can be 0 or 1) is

(a,b,c) (0,1)

Joint probability mass function is

p(a,b,c)= P(A=a, B=b, C=c)

if A,B,C are independent then

p(a,b,c)= P(A=a) P(B=b) P(C=c)

x and y are independent

P(x y)= P(x) *P(y)

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