Thread: independence of four variables

I am wondering if anyone knows the rules regarding the independence of four variables. Or a means of deriving such properties.
ie
p(A^B^C^D)= p(A)p(B)p(C)p(D), pairwise independence, etc?

I'm not sure what your question is.
Pairwise only refers to sets of two random variables.
You have four sets.

Hello,

We must have :
P(A^B)=P(A)P(B)
P(A^C)=P(A)P(C)
P(A^D)=P(A)P(D)
etc
.
.
.

P(A^B^C)=P(A)P(B)P(C)
P(A^B^D)=P(A)P(B)P(D)
P(A^C^D)=P(A)P(C)P(D)
P(B^C^D)=P(B)P(C)P(D)

P(A^B^C^D)= P(A)P(B)P(C)P(D)


In other words, you have to test the formula for any "subset" of {A,B,C,D}