The Use of Counter Examples in Learning Probability and Statistics

  1. For random events we consider the notions of a mutual independence and pairwise independence.

    2. Question: Are there sets of random events which are pairwise independent but not mutually independent?
  2. Suppose A, B, C are random events satisfying the relation:

    3. P(ABC)=P(A)P(B)P(C).

    Question: Does it follow that A, B, C are pairwise independent?