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Homework2key

# Homework2key - Homework 2(13 points due Jan 27(1.3 pts...

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1 Homework 2 (13 points) due Jan 27 (1.3 pts.) 2.4 (6-sided die)de. Suppose that one die is rolled and that you observe the number of dots facing up. From the last problem set: The sample space includes all of the possible outcomes or = {1, 2, 3, 4, 5, 6} A = {2, 4, 6} B = {4, 5, 6} C = {1, 2} D = {3} d) Determine which of the following collections of events are mutually exclusive and explain your answers: A and B, B and C, A, C, and D. A and B are not mutually exclusive because 4 and 6 are in both of them B and C are mutually exclusive because there are no elements in common. A, C and D: A and C are not mutually exclusive because 2 is in both of them, therefore A, C and D are not mutually exclusive. Note that A and D are mutually exclusive and C and D are mutually exclusive. e) Are there three mutually exclusive events amount A, B, C, and D? four? A is only mutually exclusive with D B is mutually exclusive with C and is mutually exclusive with D. As mentioned in part (d), C and D are mutually exclusive. Therefore, B, C, and D are mutually exclusive but A, B, C, and D are not. (1.5 pts.) #1. Let A, B, and C be events of a sample space. Write a mathematical expression for each of the following events. Hint: Problem 2.13 a) C occurs but B doesn't occur. C ∩ B c b) Exactly two of A, B and C occur. (A ∩ B ∩ C c ) U (A ∩ B c ∩ C) U (A c ∩ B ∩ C) The two can be either A and B, A and C or B and C c) At most one of A, B, and C occur. (A c ∩ B c ∩ C c ) U (A ∩ B c ∩ C c ) U (A c ∩ B ∩ C c ) U (A c ∩ B c ∩ C) At most one means, none occur, or A occurs or B occurs or C occurs.

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2 (3.5 pts.) 2.22. The sample space for the rolling of one 6-side die is = {1, 2, 3, 4, 5, 6}. The following table provides five different potential probability assignments to the possible outcomes. Outcome #1 #2 #3 #4 #5 1 1 / 6 0.10 0.2 ½ 1 / 16 2 1 / 6 0.15 0.2 ¼ 1 / 8 3 1 / 6 0.40 0.2 ¼ 4 1 / 6 0.05 0.2 ½ 0 5 1 / 6 0.10 0.2 - 1 / 8 7 / 16 6 1 / 6 0.20 0.2 1 / 8 1 / 8 sum 1 1 1.2 1 1 a) Which of the assignments #1 - #5 are legitimate probability assignments? Explain. #1: This is legitimate because 6 (
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Homework2key - Homework 2(13 points due Jan 27(1.3 pts...

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