2 Discrete Distributions (Bb)

2 Discrete Distributions (Bb) - Dr Harvey A Singer School...

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© 2008 by Harvey A. Singer 1 OM 210:  Statistical Analysis for  Management 2. Discrete Probability Distributions Dr. Harvey A. Singer School of Management George Mason University
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© 2008 by Harvey A. Singer 2 Learning Objectives Representation of real-world situations with well-known probability models. The distributions studied here: • Uniform • Binomial • Poisson
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© 2008 by Harvey A. Singer 3 Snap Shot Summary Uniform distribution. - All values of the r.v. are equally likely to be observed. Binomial distribution. - “Success” vs. “failure” situations. - Describes the chance of a specific number of successes in a given number of trials. Poisson distribution. - Occurrence vs. non-occurrence of an event during a specified interval. - Describes the chance of a specific number of occurrences during a given interval.
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© 2008 by Harvey A. Singer 4 Discrete Uniform Distribution Suppose the random variable consists of N values, generically denoted by x , which are all equally likely to occur. Then the probability that any one of these values x occurs is: Prob ( x ) = 1/ N - This is a restatement of the classical concept of assigning probabilities to N equally likely outcomes. So, only the name is new.
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© 2008 by Harvey A. Singer 5 Binomial Distribution Experiment with two and only two mutually exclusive outcomes. - Referred to as “success” (desired outcome) vs. “failure.” Success depends on the context of the problem and the variable of interest. Even if contrary to usual thinking. Success and failure occur in random order. - “Success” and “failure” are mutually exclusive alternatives. In any trial of the experiment or for any sampled individual, the outcome is either success or failure. One or the other, but can’t be both. Success and failure are complementary outcomes. - “Success” is the outcome that is counted.
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© 2008 by Harvey A. Singer 6 Binomial Distribution Use a “binomial” random variable that counts the number x of “successes” in a sample of n random observations or in n random trials of the experiment. The binomial distribution is used to calculate the chance of x number of successes in n random trials of the experiment.
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© 2008 by Harvey A. Singer 7 Properties and Model Assumptions Sequence of n identical random trials. Each trial has exactly 2 mutually exclusive outcomes. - “Success” (desired outcome) or “failure.” One or the other may occur but not both together. Success and failure are complementary to each other. Constant trial probability. - Probability of success is the same for all trials. Probability does not change from trial to trial. Trials are independent. - No history to phenomenon. Outcome does not depend on what has occurred before or what may occur later.
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© 2008 by Harvey A. Singer 8 Assuming the Binomial Suppose that the the random process or situation satisfies or can be assumed to satisfy the four properties of the binomial.
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2 Discrete Distributions (Bb) - Dr Harvey A Singer School...

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