pairwise independence

#1
Given a set of 0/1 random variables, I would like to determine whether
they are pairwise independent,
i.e, if P(A=1 and B=1) = P(A=1)*P(B=1).

What I find empirically from our experimental data is that P(A=1 and
B=1) >= P(A=1)*P(B=1).

Can I conclude that the set of random variables are not pairwise
independent?

Can I conclude that the set of random variables are positively
correlated?

If the test is valid, do you know how I could calculate significance
levels?

Thanks in advance.
 
E

elnaz

Guest
#2
Hello

My answer about the first question is yes, you can conclude that the set of random variables are not pairwise
independence , but when you use data so you must have a known answer , my intent is, if you find empirically from your experimental data, so u must have
P(A=1 & B=1) > P(A=1)*P(B=1) or P(A=1 & B=1)= P(A=1)*P(B=1) not P(A=1 & B=1)>= P(A=1)*P(B=1), because you compute a known number.

about another questions , do you have a set of 0/1 data as a sample of random variables ?
If you have a sample from every your random variables so you can test correlation between these variables via statistical software and Runtest is for testing independence.

A and B are variables so correlation(A,B)=cov(A,B)/{Var(A)^.5*Var(B)^.5}
={p(A=1,B=1)-P(A=1)*P(B=1)}/{Var(A)^.5*Var(B)^.5}>=0
Because u find that p(A=1,B=1)>=P(A=1)*P(B=1).