Problem 4 Let C1, C2,., CM be a partition of the sample space S, and A and B be two events. Suppose we know that • A and B are conditionally independent given C;, for all i e {1,2, -, M}; • Bis independent of all C;'s. Prove that A and B are independent.

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Problem 4
Let C1, C2, ·.., Cm be a partition of the sample space S, and A and B be two events. Suppose we
know that
• A and B are conditionally independent given C;, for all i E {1, 2, · . · , M};
• Bis independent of all C;'s.
Prove that A and B are independent.
Transcribed Image Text:Problem 4 Let C1, C2, ·.., Cm be a partition of the sample space S, and A and B be two events. Suppose we know that • A and B are conditionally independent given C;, for all i E {1, 2, · . · , M}; • Bis independent of all C;'s. Prove that A and B are independent.
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