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Section 5 Operation Management Statistics

Section 5 Operation Management Statistics - Dr Harvey A...

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© 2006 by Harvey A. Singer 1 OM 210:  Statistical Analysis for  Management 1. Discrete Random Variables Dr. Harvey A. Singer School of Management George Mason University
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© 2006 by Harvey A. Singer 2 Learning Objectives Introduce the concept of random variables. To generalize basic probability to quantitative events. Where the “events” are counts or measured values. Characterize discrete random variables. In terms of their expected value, variance, and standard deviation. Use CV to determine how good the expected value is at being the single-number representation of the random variable. Use expected values as criteria in decision making. Introduce discrete probability distributions. “Empirical” distributions to describe individual, specific, random situations.
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© 2006 by Harvey A. Singer 3 Definition A random variable (r.v.) is a variable representing a given situation or quantity of interest, which has different numerical values representing the different possible random outcomes (or events). A random variable is a variable which takes on a numerical value as the consequence of a random result. A random variable is a variable whose numerical value is assigned according to the outcome of a random experiment.
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© 2006 by Harvey A. Singer 4 Why Random Variables? Very often have numeric data rather than narrative events. Very often want to know the chance of occurrence of the number of different outcomes (of similar events) rather than the probability of the specific individual outcomes. E.g., the number of heads in 3 flips of a coin. Without knowing the order in which the heads may come up. Use a “discrete” random variable that counts the number of events. Very often want to the chance of occurrence of a value occurring within continuous ranges of possible values. E.g., what is the chance of randomly selecting a person who weighs between 140 and 160 pounds. Use a “continuous” random variable.
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© 2006 by Harvey A. Singer 5 Why Random Variables? Very often want to know what to expect from a random situation. The concepts of basic probability can’t do this. Define a random variable and borrow the concepts from descriptive analysis to calculate the expected value. Very often want to know the variability between outcomes of a random situation. The concepts of basic probability can’t do this. Define a random variable and borrow the concepts from descriptive analysis to calculate variance.
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© 2006 by Harvey A. Singer 6 Types of Random Variables Discrete vs. continuous. A random variable is discrete if and only if it can take on no more than a countable number of distinct integer values. Results from a counting process.
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