# Statistics

Feb 3rd, 2012
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Question and answers. Suppose that a number x is to be selected from the real line S, and let A, B, and C be the events represented by the following subsets of S, where the notion {x|⋯} denote the set containing every point x for which the property presented following the colon is satisfied: A={x|1≤x≤5} B={x|3

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1. Suppose that a number x is to be selected from the real line S, and let A, B, and C be the events represented by the following subsets of S, where the notion denote the set containing every point x for which the property presented following the colon is satisfied:.Describe each of the following events as a set of real numbers:(a) which means x is lying in the interval 1 and 5 therefore Ac= where x takes the value x or x>5.(b) Answer: Given that and therefore A(c) Answer: Given that and therefore Cc=Hence =B=(a) Given that , and therefore Ac=, Bc= and Cc=.Hence =(a) Given that , and therefore A and , hence ={} where {} is the null set.2. (a) How many three-digit numbers can be formed form the digits 0, 1, 2, 3, 4, 5, and 6, if each digit can be used only once?Answer: 1st digit can be any number from 1-6 (6 choices) 2nd digit can be any number (including zero this time and the number that you did not choose for the first digit) (6 choices) 3rd digit (has to be distinct from the other two numbers) [5 choices for the last digit] Using the multiplication principle answer = 6* 6*5 = 180 180 ways to create the 3 digit numbers using those numbers.(b) How many these are odd numbers?Answer: The problem says that we have to choose 3 odd - digit numbers from 0,1,2,3,4,5 and 6 if each digit can only be used once. The last digit can be chosen in 3 ways(1,3,5) so we have 3 choices for the last digit. First digit can

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