independence

1. I Are these events independent?

Hello everyone. Let us consider 3 events A,B,C such that: $$P((A \cap B )\cup C)=P(A)*P(B)*P(C)$$ Notice that the second term is a union and not an intersection. Are they independent? And what if the assumption was: $$P(A \cap( B \cup C))=P(A)*P(B)*P(C)$$? I know that the independence condition...
2. I (In)dependence in entanglement experiments

If an entanglement experiment, whereby an entangled pair of particles is measured at both ends, is independent of the next entanglement experiment with another pair of entangled particles, how can there be a correlation? It seems that each independent run does not influence the next run, but...
3. B Conditional Probability, Independence, and Dependence

(Mentor note: link removed as not essential to the question.) The problem is: what is relevance anyhow? My questions are these: did I get the math right in the following? Is there a better, more acceptable way to lay out the sample space Ω and the two events F and E? Apart from the math...
4. Marginal PMG of of 2 random variables with Joint PMF

1. Homework Statement Consider two random variables X and Y with joint PMF given by: PXY(k,L) = 1/(2k+l), for k,l = 1,2,3,.... A) Show that X and Y are independent and find the marginal PMFs of X and Y B) Find P(X2 + Y2 ≤ 10) 2. Homework Equations P(A)∩P(B)/P(B) = P(A|B) P(A|B) = P(A) if...