Chapter 4 Commonly Used Distributions Introduction Statistical inference involves drawing a sample from a population and analyzing the sample data to learn about the population. In many situations, one has some knowledge about the probability mass function...
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Chapter 4 Commonly Used Distributions Introduction Statistical inference involves drawing a sample from a population and analyzing the sample data to learn about the population. In many situations, one has some knowledge about the probability mass function or probability density function of the population. In particular, the probability mass or density function can often be well approximated by one of several standard families of curves, or functions. In this chapter, we describe some of these standard families, and for each one we describe some conditions under which it is an appropriate model. 4.1 The Binomial Distribution Imagine an experiment that can result in one of two outcomes. One outcome is labeled “success”andtheotheroutcomeislabeled“failure.”Theprobabilityofsuccessisdenoted by p. The probability of failure is therefore 1− p. Such a trial is called a Bernoulli trial with success probability p. The simplest Bernoulli trial is the toss of a coin. The two outcomes are heads and
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