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# Ch7 Discreate Probability.pdf

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Department
Course
Professor
Nabil Ayoub
Semester
Winter

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Chapter 7: Random Variables & Discrete Probability Distributions 7.1 Random Variables & Probability Distributions Random Variable: “is a function or rule that assigns a number to each outcome of an experiment” (ex. Instead of talking about the coin flipping event as {heads, tails} think of it as the number of heads when flipping a coin{1, 0} - numerical events) Probability distribution is a table, formula, or graph that describes the values of a random variable and the probability associated with these values. Probability Notation: P( = ), represent the name of the random variable and represent the value of the random variable. more simply we use P(x) Since we’re describing a random variable (discrete or continuous) we have two types of probability distributions:  Discrete Probability Distribution, (Ch7) one that takes on a countable number of values (integers: e.g. values on the rolling of dice: 2, 3, …, 12)  Continuous Probability Distribution (Ch8) one whose values are not discrete, not countable. (real numbers: e.g. time: 3.5 min, distance: 15.27 mm, …) Discrete Probability Distribution: The probabilities of the values of a discrete random variable may be derived by means of probability tools such as tree diagrams or by applying one of the definitions of probability, so long as these two conditions apply: 1. 0 ≤ P(X) ≤ 1 2. ⅀ P(x) = 1, for all x Example 7.1 (p.220): The Statistical Abstract of the United States is published annually. It contains a wide variety of information based on the census as well as other sources. The objective is to provide information about a variety of different aspects of the lives of the country’s residents. One of the questions asks households to report the number of persons living in the household. The following table summarizes the data. Develop the probability distribution of the random variable defined as the number of persons per household. o What is the probability that, selecting a household at random, has 4 persons? o What is the probabilit
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