Introduction to Set Theory

Introduction to Set Theory - Introduction to Set Theory...

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Introduction to Set Theory (and brief discussion of probability) Population- the collection of all individuals or items under consideration In this course we denote population by (the capital letter omega). Example: If we roll a die one time, then ={1,2,3,4,5,6}. represents all POSSIBLE OUTCOMES from the “random experiment” or the model under consideration. Loosely speaking, probability is a percentage. More specifically, we have the following concept: Suppose that a member is selected at random from a finite population. Then the probability that the member obtained has a specified attribute equals the percentage of the population that has that attribute. Example: Suppose a Stat 225 class consists of 30 males and 10 females. What is the probability that a random selected student [from this particular Stat 225 class] is male? Random Experiment- an action whose outcome cannot be predicted with certainty (there is some randomness involved in the action). Event- some SPECIFIED result that may or may not occur when the random experiment is performed. Remember, an event can be simple (only one specified result) or it can be a collection of results. (The class example of rolling a die: A-5 is rolled, B- 3 is rolled, C- an odd is rolled. A and B are simple events but C is not). Frequentist Interpretation of Probability The probability of an event is the long-run proportion of times that the event occurs in independent repetitions of the random experiment. (Independence is a key topic in probability.) This can be written as: N(E) P(E) n . The n represents the sample size. P(E) is the probability of event E occurring (p or P always represent probability; when clarification is not needed we will just use p). N(E)
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Introduction to Set Theory - Introduction to Set Theory...

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