Search for tag: "mean"

20 Media

Estimation and Prediction for a Specific Value of… duration 18 minutes 16 seconds Estimation and Prediction for a Specific Value of… Estimation and Prediction for a Specific Value of x	Estimation and Prediction for a Specific Value of x In this final topic, we consider using the estimated regression line to estimate the mean response at a given value of the explanatory (x) variable. The standard error of this estimated mean… mean response prediction confidence interval for the mean response standard error of the estimation mean response prediction interval standard error of prediction derived distributions From Jane Harvill 114 plays 0
Introduction to Oneway Analysis of Variance… duration 19 minutes 8 seconds Introduction to Oneway Analysis of Variance… Introduction to Oneway Analysis of Variance (ANOVA)	Introduction to Oneway Analysis of Variance (ANOVA) Up until now, we have modeled random variables with a probability mass function or a probability density function. We then discussed in detail the theory behind inference on the unknown parameters. … cell means model overall mean treatment effects model identifiability From Jane Harvill 83 plays 0
Find the Bayes estimator of the rate of a Poisson… duration 11 minutes 12 seconds Find the Bayes estimator of the rate of a Poisson… Find the Bayes estimator of the rate of a Poisson distribution	Find the Bayes estimator of the rate of a Poisson distribution This example illustrates how to find the Bayes estimator, under squared error loss function, of the rate of a Poisson distribution if the prior distribution on the rate is a gamma distribution. bayes estimator parameter space support prior distribution posterior distribution marginal distribution posterior mean gamma distribution From Jane Harvill 233 plays 0
Evaluating Point Estimators: Bias and Mean… duration 18 minutes 24 seconds Evaluating Point Estimators: Bias and Mean… Evaluating Point Estimators: Bias and Mean Squared Error	Evaluating Point Estimators: Bias and Mean Squared Error The first two criteria for evaluating point estimators are the bias of the estimator and the mean squared error of the estimator. The goal is to chose the estimator with the smallest mean squared… bias variance mean squared error From Jane Harvill 653 plays 0
Sampling from a Normal Distribution duration 47 minutes 27 seconds Sampling from a Normal Distribution Sampling from a Normal Distribution	Sampling from a Normal Distribution In previous lessons, properties of samples and of statistics computed on a random sample were discussed under a very general framework; in other words, under the idea that a random sample is selected… normal population linear combinations of normal random variables chi-squared distribution student's t distribution snedecor's f distribution independent sample mean sample variance From Jane Harvill 87 plays 0
Sums of Random Variables from a Random Sample duration 36 minutes 55 seconds Sums of Random Variables from a Random Sample Sums of Random Variables from a Random Sample	Sums of Random Variables from a Random Sample When a random sample is drawn, some summary of the values is usually computed. Any well-defined summary may be expressed mathematically as a function of an n-dimension vector. The domain of that… random sample iid statistic sampling distribution unbiased estimator location-scale family exponential family sample mean sample variance sample standard deviation From Jane Harvill 184 plays 0
Location-Scale Families duration 11 minutes 42 seconds Location-Scale Families Location-Scale Families	Location-Scale Families We discuss three techniques for constructing families of distributions. The resulting families have ready physical interpretations that make them useful for modeling as well as convenient… standard probability density function location family location parameter scale family scale parameter location-scale family inverse transformation mean variance From Jane Harvill 410 plays 0
Beta Distribution duration 9 minutes 19 seconds Beta Distribution Beta Distribution	Beta Distribution 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… beta distribution probability density function cumulative distribution function mean variance shape parameter beta function nth moment From Jane Harvill 47 plays 0
Normal Distribution duration 25 minutes 42 seconds Normal Distribution Normal Distribution	Normal Distribution 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… normal distribution probability density function cumulative distribution function mean variance moment generating function binomial distribution empirical rule standard normal distribution standardized variable z-score From Jane Harvill 63 plays 0
Gamma Distribution duration 17 minutes 36 seconds Gamma Distribution Gamma Distribution	Gamma Distribution 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… gamma distribution cumulative distribution function probability density function mean variance moment generating function poisson distribution exponential distribution chi-squared distribution From Jane Harvill 258 plays 0
Uniform Distribution duration 10 minutes 52 seconds Uniform Distribution Uniform Distribution	Uniform Distribution 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… uniform distribution probability density function cumulative distribution function mean variance moment generating function From Jane Harvill 77 plays 0
Continuous Distributions: A Review duration 8 minutes 22 seconds Continuous Distributions: A Review Continuous Distributions: A Review	Continuous Distributions: A Review 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. continuous random variable cumulative distribution function probability density function expected value mean variance moment generating function discrete random variable From Jane Harvill 61 plays 0
Poisson Distribution duration 11 minutes 45 seconds Poisson Distribution Poisson Distribution	Poisson Distribution 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… poisson distribution probability mass function cumulative distribution function moment generating function mean variance rate approximation From Jane Harvill 53 plays 0
Hypergeometric Distribution duration 23 minutes 14 seconds Hypergeometric Distribution Hypergeometric Distribution	Hypergeometric Distribution The experiment that is used to illustrate when the hypergeometric distribution arises is that of an urn with N balls of two colors; M "white" balls and N - M "black" balls. The… hypergeometric distribution binomial approximation mean variance urn sampling without replacement From Jane Harvill 88 plays 0
Geometric Distribution duration 17 minutes 46 seconds Geometric Distribution Geometric Distribution	Geometric Distribution Like the binomial and hypergeometric distributions, the geometric distribution is related to the Bernoulli(p) distribution. Unlike the binomial and hypergeometric distributions, the geometric… geometric distribution geometric series probabiity mass function cumulative distribution function moment generating function mean variance memoryless From Jane Harvill 47 plays 0
Binomial Distribution duration 43 minutes 3 seconds Binomial Distribution Binomial Distribution	Binomial Distribution 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… bernoulli process binomial distribution binomial theorem mean variance moment generating function mutually independent From Jane Harvill 77 plays 0
Bernoulli Distribution duration 10 minutes 45 seconds Bernoulli Distribution Bernoulli Distribution	Bernoulli Distribution 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… bernoulli distribution bernoulli experiment bernoulli random variable mean variance moment generating function probability mass function cumulative distribution function From Jane Harvill 58 plays 0
Discrete Uniform Distribution duration 14 minutes 19 seconds Discrete Uniform Distribution Discrete Uniform Distribution	Discrete Uniform Distribution 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… discrete uniform distribution mean variance moment generating function parameters parameter space From Jane Harvill 89 plays 0
Discrete Distributions: A Review duration 11 minutes 53 seconds Discrete Distributions: A Review Discrete Distributions: A Review	Discrete Distributions: A Review In this lesson, a brief review of the general properties of discrete distributions is provided. discrete distribution probability mass function cumulative distribution function mean variance moment generating function From Jane Harvill 52 plays 0
Moments duration 22 minutes 42 seconds Moments Moments	Moments In this lesson, moments, central moments, the mean and variance of a distribution are defined and illustrated. central moment moment mean variance From Jane Harvill 67 plays 0