Test independence: Given P(X)=0.4P(X)=0.4P(X)=0.4, P(Y)=0.5P(Y)=0.5P(Y)=0.5, P(X∩Y)=0.2P(X \cap Y)=0.2P(X∩Y)=0.2. Are X and Y independent?
Yes, P(X)P(Y)=0.2P(X)P(Y) = 0.2P(X)P(Y)=0.2
No, P(X)P(Y)=0.2P(X)P(Y) = 0.2P(X)P(Y)=0.2 but P(X∩Y)=0.15P(X \cap Y) = 0.15P(X∩Y)=0.15 elsewhere
Yes, they satisfy P(X∣Y)=P(X)P(X|Y) = P(X)P(X∣Y)=P(X)
Cannot determine