OPR201-chapter2-slide.pdf - Sample Space and Events Counting Sample Points Probability of an Event Conditional Probability the Product Rule and

OPR201-chapter2-slide.pdf - Sample Space and Events...

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Sample Space and Events Counting Sample Points Probability of an Event Conditional Probability, the Product Rule, and Independence Bayes’ Rule Chapter 2: Probability Department of Engineering Sciences Izmir Katip Celebi University Chapter 2: Probability
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Sample Space and Events Counting Sample Points Probability of an Event Conditional Probability, the Product Rule, and Independence Bayes’ Rule Sample Space and Events Chapter 2: Probability
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Sample Space and Events Counting Sample Points Probability of an Event Conditional Probability, the Product Rule, and Independence Bayes’ Rule In the study of statistics, we are concerned basically with the presentation and interpre- tation of chance outcomes that occur in a planned study or scientific investigation. For example, we may record the number of accidents that occur monthly at the intersection of Driftwood Lane and Royal Oak Drive, hoping to justify the installation of a traffic light; we might classify items coming off an assembly line as "defective" or "nondefective"; or we may be interested in the volume of gas released in a chemical reaction when the concentration of an acid is varied. Hence, the statistician is often dealing with either nu- merical data , representing counts or measurements, or categorical data , which can be classified according to some criterion. We shall refer to any recording of information, whether it be numerical or categorical, as an observation . Thus, the numbers 2, 0, 1, and 2, representing the number of accidents that occurred for each month from January through April during the past year at the intersection of Driftwood Lane and Royal Oak Drive, constitute a set of observations. Similarly, the categorical data N , D , N , N , and D , representing the items found to be defective or nondefective when five items are inspected, are recorded as observations. Chapter 2: Probability
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Sample Space and Events Counting Sample Points Probability of an Event Conditional Probability, the Product Rule, and Independence Bayes’ Rule Statisticians use the word experiment to describe any process that generates a set of data. A simple example of a statistical experiment is the tossing of a coin. In this experiment, there are only two possible outcomes, heads or tails. Another experiment might be the launching of a missile and observing of its velocity at specified times. We are particularly interested in the observations obtained by repeating the experiment several times. In most cases, the outcomes will depend on chance and, therefore, cannot be predicted with certainty. If a chemist runs an analysis several times under the same conditions, he or she will obtain different measurements, indicating an element of chance in the experimental procedure. Even when a coin is tossed repeatedly, we cannot be certain that a given toss will result in a head. However, we know the entire set of possibilities for each toss.
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