Describe the difference between marginal independence and conditional independence.
For variables X and Y, if P (X|Y) = P (X) then X is marginally independent of Y. That is, knowing the value of Y doesn't change the probability of X. For conditional independence, if P (X|Y, Z) = P (X|Z) then X is conditionally independent of Y given Z. In other words, if you know the value of Z, knowing the value of Y doesn't tell you anything more about X.