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2) We say that a collection of N random variables Z1, ..., ZN (we will assume here that these r.v.'s are either all discrete or all continuous) is mutually independent if we have fz1,..,ZN (Z1, ..., ZN) = fz, (21) ... fZN (ZN), for all admissible choices of the z1, ..., Zy, where the fz, , ..., fzy, and fz1,...,ZN are probability density functions if Z1, ..., Zy are continuous r.v.'s and are probability mass functions if the Z1, ..., Zy are discrete r.v.'s. Moreover, these N variables Z1, ..., ZN are instead said to be pairwise independent if any two variables chosen from this collection of N r.v.'s are independent. a) Does pairwise independence imply mutual independence? Prove or disprove. b) Does mutual independence imply pairwise independence? Prove or disprove