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hw1 - IE 336 Sep 5 2008 Handout#2 Due Sep 12 2008 Homework...

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IE 336 Handout #2 Sep. 5, 2008 Due Sep. 12, 2008 Homework Set #1 1. Let B 1 , B 2 , . . . , B n be a partition of the sample space of a random experiment. Using the axioms 1 - 3 show that P ( A ) = n X i =1 P ( A | B i ) P ( B i ) where A is an event from the sample space. ( Hint: Try considering A ( B 1 B 2 ∪· · ·∪ B n ) = ( A B 1 ) ( A B 2 ) ∪ · · · ∪ ( A B n ).) 2. There is a box with two black balls, numbered 1 , 2, and two white balls numbered 3 , 4. One ball from the box is selected at random. Let A , B , and C denote the events in the following way: A black ball is selected B odd-numbered ball is selected C number of the selected ball is greater than 2. Clearly, A = { 1 , 2 } . (a) Determine B and C . (b) Are events A and B independent? Explain.
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