Lecture_week1 - ISyE 2027 Probability with Applications...

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ISyE 2027 Probability with Applications Polly B. He Fall10, Week 1 What’s to be covered: Administrative Notes Chapter 2: Sample space, Events, Probability Sets and Operations on them Counting What is this course about? Think about things that are random and those that are not. Which one can you name more? Language to describe random experiments Sample spaces are sets whose elements describe the outcomes of the experiment in which we are interested. Example 2.1(a) Two possible outcomes from a single coin toss (if ignoring the possibility that the coin lands on the edge): Ω = { H, T } . Example 2.1(b) The month in which the birthday of the next person you meet on the street falls: Ω = { Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec } . Events are subsets of the sample space. We say that an event A occurs if the outcome of the experiment is an element of the set A . Example 2.2(a) In the experiment of Example 2.1(a), we can ask for the outcomes that correspond to a long month (with 31 days): L = { Jan, Mar, May, Jul, Aug, Oct, Dec } . Example 2.2(b) As in the previous example, we may ask for the outcomes that correspond to months that have the letter r in their (full) name: R = { Jan, Mar, Oct, Dec } . Intersection of sets Example 2.2(c) If both L and R occur, the set L R is called the intersection of L and R . L R = 1
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Union of sets Example 2.2(d) If at least one of the events A and B occurs, we have the union A B of the two sets A and B . L R = Complement of A : if and only if A does not occur. A c = { ω Ω : ω / A } . For example, L c = The empty set is the complement of Ω, denoted as . If events A and B have no outcomes in common, i.e., A B = , then A and B are disjoint or mutually exclusive .
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Lecture_week1 - ISyE 2027 Probability with Applications...

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