13. (a) If A and B are independent events, prove that A and B are independent. (b)...
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13.
(a) If A and B are independent events, prove that A and B are independent.
(b) Suppose A1, A2, . . . , An are independent. Prove by induction on n that A ¯ 1, A2, . . . , An are independent.
(c) Suppose A1, A2, . . . , An are independent. Prove that A1, . . . , Ak, Ak+1, . . . , An are independent, for all k, 1 ≤ k ≤ n and all n
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