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Statistics
Transform Methods
(m23473)
Author:
Paul E Pfeiffer
Keywords:
Center of mass
,
Characteristic function
,
Generating function
,
Independence
,
Integral transforms
,
Laplace transform
,
Moment generating function
,
Moments
,
Operational properties
,
Simple random variables
,
Spread of the distribution
,
Transforms
,
Uncorrelated
Summary:
The mathematical expectation E[X] of a random variable locates the center of mass for the induced distribution, and the expectation of the square of the distance between X and E[X] measures the spread of the distribution about its center of mass. These quantities are also known, respectively, as ... random variables.
[Expand Summary]
The mathematical expectation E[X] of a random variable locates the center of mass for the induced distribution, and the expectation of the square of the distance between X and E[X] measures the spread of the distribution about its center of mass. These quantities are also known, respectively, as the mean (moment) of X and the variance or second moment of X about the mean. Other moments give added information. We examine the expectation of certain functions of X. Each of these functions involves a parameter, in a manner that completely determines the distribution. We refer to these as transforms. In particular, we consider three of the most useful of these: the moment generating function, the characteristic function, and the generating function for nonnegative, integervalued random variables.
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
74.35%
Revised:
20090918
Revisions:
8
Popularity is measured as percentile rank of page views/day over all time
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