Q1 Solutions

Q1 Solutions - P A ∪ B = P A P B for each A B ∈ E such...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Fall, 2007) Quiz 1 Solutions (Wednesday, September 26) Question 1. Write down the sample space for the sum of 3 coins, where a heads counts as 2 and a tails counts as 0 . S = { 0 , 2 , 4 , 6 } . (1) Question 2. Write down the set of all possible events for this sample space. E = {∅ , { 0 } , { 2 } , { 4 } , { 6 } , { 0 , 2 } , { 0 , 4 } , { 0 , 6 } , { 2 , 4 } , { 2 , 6 } , { 4 , 6 } , { 0 , 2 , 4 } , { 0 , 2 , 6 } , { 0 , 4 , 6 } , { 2 , 4 , 6 } , { 0 , 2 , 4 , 6 }} . (2) Question 3. State the three axioms of probability. Axiom 1. Probabilities are not negative: P ( A ) 0 for each event A ∈ E . Axiom 2. Something must happen: P ( S ) = 1. Axiom 3. The probability of the union of two disjoint events is the sum of the probabilities of the two events:
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Unformatted text preview: P ( A ∪ B ) = P ( A ) + P ( B ), for each A, B ∈ E such that A ∩ B = ∅ . Question 4. Let A, B be two events on a sample space S . Draw the Venn diagram for A ∩ B , A ∪ B , A ∩ B (use separate diagrams for each). A ∩ B is the intersection of the two circles, A ∪ B is the union of the two circles, and A ∩ B is the intersection of A with the complement of B . www.ece.drexel.edu/faculty/sweber 1 September 26, 2007...
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This note was uploaded on 04/05/2010 for the course ENGR 361 taught by Professor Eisenstein during the Spring '04 term at Drexel.

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