PickingTheCorrectDistribution

# PickingTheCorrectDistribution - Picking the Correct...

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Picking the Correct Distribution Binomial, Negative Binomial, Geometric, or Hypergeometric? Students often become confused when trying to decide whether a random variable in a word problem fits a binomial distribution, negative binomial, geometric or hypergeometric. This paper will explain the similarities and differences between these four related distributions. First, a binomial random variable must have n independent trials, they must be Bernoulli trials (i.e., two choices only. ..1 or 0, heads or tails, yes or no, etc.), and the probability of a "success" must be the same on each trial. We call the probability of success p . In order for the probability of success p to be constant, this means that we are sampling from a very large population, so that picking one sample does not materially affect the probability of success on the next sample. An example of a very large population would be the population of all fish in Lake Superior. The population is large enough that taking a few fish out of the lake, even without replacing them, does not materially affect the probabilities on the next pick. A binomial random variable can tell us the probability of obtaining k successes out of n trials. For example, if we pick 20 people out of a large population, and we know that there is a probability of 40% that any given member of the population smokes, we can define a random variable X

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PickingTheCorrectDistribution - Picking the Correct...

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