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Oftentimes when two random variables (X, Y) are observed, the values of the two variables are related. For example, it may be that knowledge about the value of X gives information about the value of…
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The beta distribution is the last continuous distribution we will discuss. Like the gamma distribution, the beta distribution earns its name from being associated with the beta function. The beta…
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In this lesson, we learn about the most important distribution in statistics - the normal distribution. We investigate the probability density function and cumulative distribution function and the…
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The gamma family of distributions is a very special family that has many distributions as a specific case. In this lesson, we begin with the gamma function. We then introduce the gamma…
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An overview of the uniform distribution is given, including its probability density function (PDF) and cumulative distribution function (CDF). The mean, variance, and moment generating function are…
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In this lesson, a brief review of the general properties of continuous distributions is provided. The end of the lesson is a comparison of the properties for continuous and discrete distributions.
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The Poisson distribution is different from all of the discrete distributions we have considered up until this point. Instead of counting the number of "successes" or counting the number of…
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The negative binomial distribution is an extension of the geometric distribution, and so is also related to the Bernoulli distribution. Whereas the geometric distribution results from counting the…
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Like the binomial and hypergeometric distributions, the geometric distribution is related to the Bernoulli(p) distribution. Unlike the binomial and hypergeometric distributions, the geometric…
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The binomial distribution is introduced through its unique connection to the Bernoulli distribution through what is called a Bernoulli process. The probability mass function is derived and proven to…
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The Bernoulli and binomial distributions are used for modeling a dichotomous experiment or a sequence of independent dichotomous experiments, respectively. Alone, both distributions apply to a wide…
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The discrete uniform distribution is one of the simplest discrete distributions. In this lesson, the distribution is defined via its probability mass function. The cumulative distribution function…
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In this lesson, a brief review of the general properties of discrete distributions is provided.
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In this video, the moment generating (MGF) is defined. Its utility for finding the moments of a distribution is presented and illustrated. Following two examples, the use of the MGF for equating…
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In this lesson, moments, central moments, the mean and variance of a distribution are defined and illustrated.
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September 26, 2017 - Truett's Pastor of the Day presented by the Kyle Lake Center for Effective Preaching
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