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File:High_School_Probability_and_Statistics_(Advanced).pdf Licensing This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
The fourth central moment is a measure of the heaviness of the tail of the distribution. Since it is the expectation of a fourth power, the fourth central moment, where defined, is always nonnegative; and except for a point distribution, it is always strictly positive. The fourth central moment of a normal distribution is 3σ 4.
Specifically, it reflects either the presence of existing outliers (for sample kurtosis) or the tendency to produce outliers (for the kurtosis of a probability distribution). The underlying logic is straightforward: Kurtosis represents the average (or expected value) of standardized data raised to the fourth power. Standardized values less than ...
File:High_School_Probability_and_Statistics_(Basic).pdf Licensing This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Download as PDF; Printable version; ... Probability and Statistics, 4th Ed, Pearson, ... Student Solutions Manual for Probability and Statistics, Pearson, ISBN ...
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, [1] is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability =.
In probability theory and statistics, a central moment is a moment of a probability distribution of a random variable about the random variable's mean; that is, it is the expected value of a specified integer power of the deviation of the random variable from the mean. The various moments form one set of values by which the properties of a ...
In probability theory and statistics, a standardized moment of a probability distribution is a moment (often a higher degree central moment) that is normalized, typically by a power of the standard deviation, rendering the moment scale invariant. The shape of different probability distributions can be compared using standardized moments. [1]
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