01_21ans - STAT 400 Examples for Spring 2011 1 Suppose a...

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Unformatted text preview: STAT 400 Examples for 01/21/2011 Spring 2011 1. Suppose a 6-sided die is rolled. The sample space, S , is { 1, 2, 3, 4, 5, 6 } . Consider the following events: A = { the outcome is even } , B = { the outcome is greater than 3 } , a) List outcomes in A, B, A ' , A ∩ B, A ∪ B. A = { the outcome is even } = { 2, 4, 6 }, B = { the outcome is greater than 3 } = { 4, 5, 6 }, A ' = { 1, 3, 5 }, A ∩ B = { 4, 6 }, A ∪ B = { 2, 4, 5, 6 }. b) Find the probabilities P( A ), P( B ), P( A ' ), P( A ∩ B ), P( A ∪ B ) if the die is balanced (fair). P( A ) = 3 / 6 , P( B ) = 3 / 6 , P( A ' ) = 3 / 6 , P( A ∩ B ) = 2 / 6 , P( A ∪ B ) = 4 / 6 . c) Suppose the die is loaded so that the probability of an outcome is proportional to the outcome, i.e. P( 1 ) = p , P( 2 ) = 2 p , P( 3 ) = 3 p , P( 4 ) = 4 p , P( 5 ) = 5 p , P( 6 ) = 6 p . i) Find the value of p that would make this a valid probability model....
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This note was uploaded on 02/24/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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01_21ans - STAT 400 Examples for Spring 2011 1 Suppose a...

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