Let X₁, X₂ be independent and identically distributed random variables following a geometric distribution with parameter p = (0, 1), that is, P(X₁ = k) = pk-¹ (1-p) for k = N. a) Derive a formula for P(X₁2 k) for k € N. b) Determine the cumulative distribution function of Y= min(X₁, X₂). c) Let Z= max(X₁, X₂). Are Y and Z independent? Justify your answer.

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