Normal Distribution
... rule) applies to all Normal Distributions. It dictates the following: - 68% of all observations fall within one standard deviation of the mean - 95% of all observations fall within two standard deviations of the mean - 99.7% of all observations fall within three standard deviations of the mean ...
... rule) applies to all Normal Distributions. It dictates the following: - 68% of all observations fall within one standard deviation of the mean - 95% of all observations fall within two standard deviations of the mean - 99.7% of all observations fall within three standard deviations of the mean ...
Continuous Distributions (Uniform, Normal, Exponential) PowerPoint
... provide a measure of average value and degree of variation from the average value • If random samples of size n are drawn from the population, then it can be shown (the Central Limit Theorem) that the distribution of the sample means approximates that of a distribution with mean: μ = m and σ. s stan ...
... provide a measure of average value and degree of variation from the average value • If random samples of size n are drawn from the population, then it can be shown (the Central Limit Theorem) that the distribution of the sample means approximates that of a distribution with mean: μ = m and σ. s stan ...
Statistics for the Social Science
... The Poisson random variable, X ~ Poisson(), is often used to count the number of events of a certain type that occurs in a fixed period (e.g. industrial accidents in a factory each month, hypoglaecaemic episodes experienced by someone with diabetes in a year). If X ~ Poisson() then E(X) = and V ...
... The Poisson random variable, X ~ Poisson(), is often used to count the number of events of a certain type that occurs in a fixed period (e.g. industrial accidents in a factory each month, hypoglaecaemic episodes experienced by someone with diabetes in a year). If X ~ Poisson() then E(X) = and V ...
PowerPoint Slides that accompany the lecture
... • 2nd VARS • normalcdf(2.26, 10) • NOTE: The 10 is just giving a very large value because we cannot tell the calculator where to stop or to go to infinity. ...
... • 2nd VARS • normalcdf(2.26, 10) • NOTE: The 10 is just giving a very large value because we cannot tell the calculator where to stop or to go to infinity. ...
Central limit theorem
In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution. That is, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution (commonly known as a ""bell curve"").The central limit theorem has a number of variants. In its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, given that they comply with certain conditions.In more general probability theory, a central limit theorem is any of a set of weak-convergence theorems. They all express the fact that a sum of many independent and identically distributed (i.i.d.) random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. When the variance of the i.i.d. variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i.i.d. random variables with power law tail distributions decreasing as |x|−α−1 where 0 < α < 2 (and therefore having infinite variance) will tend to an alpha-stable distribution with stability parameter (or index of stability) of α as the number of variables grows.