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Author: Paul E Pfeiffer

Keywords: Basic sequence, Compound demand, Counting random variable, Counting random variables, Incremental sequence, Matlab and compound demand, Random sums

Summary: The usual treatments deal with a single random variable or a fixed, finite number of random variables, considered jointly. However, there are many common applications in which we select at random a member of a class of random variables and observe its value, or select a random number of random ... various situations.

Subject:	Mathematics and Statistics
Language:	English
Popularity:	38.16%
Revised:	2009-09-18
Revisions:	6

Random Signals (m10989)

Author: Nick Kingsbury

Keywords: random signals

Summary: This module introduces random signals.

Subject:	Mathematics and Statistics
Language:	English
Popularity:	91.28%
Revised:	2005-06-07
Revisions:	6

Random Signals and Noise (m31819)

Author: Phil Schniter

Keywords: autocorrelation, expectation, filtering, noise, power spectral density, power spectrum, PSD, random process, random signal, uncorrelated, white noise, wide-sense stationary, zero-mean

Summary: This module describes the basics of random signals and noise as needed for an introductory course on data communications. First it introduces the notion of power spectral density (PSD) and defines "white" noise as a noise with a flat PSD. Next it describes the effect that linear filtering has on ... fundamental properties.

Subject:	Mathematics and Statistics
Language:	English
Popularity:	53.38%
Revised:	2009-09-16
Revisions:	3

Random Variables and Probabilities (m23260)

Author: Paul E Pfeiffer

Keywords: applied probability, mapping, probability, random variables,

Summary: Often, each outcome of an experiment is characterized by a number. If the outcome is observed as a physical quantity, the size of that quantity (in prescribed units) is the entity actually observed. In many nonnumerical cases, it is convenient to assign a number to each outcome. For example, in ... probability analysis. Often, each outcome of an experiment is characterized by a number. If the outcome is observed as a physical quantity, the size of that quantity (in prescribed units) is the entity actually observed. In many nonnumerical cases, it is convenient to assign a number to each outcome. For example, in a coin flipping experiment, a “head” may be represented by a 1 and a “tail” by a 0. In a Bernoulli trial, a success may be represented by a 1 and a failure by a 0. In a sequence of trials, we may be interested in the number of successes in a sequence of n component trials. One could assign a distinct number to each card in a deck of playing cards. Observations of the result of selecting a card could be recorded in terms of individual numbers. In each case, the associated number becomes a property of the outcome. The fundamental idea of a real random variable is the assignment of a real number to each elementary outcome ω in the basic space Ω. Such an assignment amounts to determining a function X, whose domain is Ω and whose range is a subset of the real line R. Each ω is mapped into exactly one value t, although several ω may have the same image point. Except in special cases, we cannot write a formula for a random variable X. However, random variables share some important general properties of functions which play an essential role in determining their usefulness. Associated with a function X as a mapping are the inverse mapping and the inverse images it produces. By the inverse image of a set of real numbers M under the mapping X, we mean the set of all those ω∈Ω which are mapped into M by X. If X does not take a value in M, the inverse image is the empty set (impossible event). If M includes the range of X, (the set of all possible values of X), the inverse image is the entire basic space Ω. The class of inverse images of the Borel sets on the real line play an essential role in probability analysis.

Subject:	Mathematics and Statistics
Language:	English
Popularity:	59.01%
Revised:	2009-09-18
Revisions:	9

Random Variables and Probability Density Functions (m11246)

Author: Don Johnson

Subject:	Mathematics and Statistics, Science and Technology
Language:	English
Popularity:	87.44%
Revised:	2003-08-01
Revisions:	2

Random Vectors (m11249)

Author: Don Johnson

Subject:	Mathematics and Statistics, Science and Technology
Language:	English
Popularity:	74.90%
Revised:	2003-08-08
Revisions:	2

Random Vectors (m10988)

Author: Nick Kingsbury

Keywords: random vectors

Summary: This module introduces random vectors.

Subject:	Mathematics and Statistics
Language:	English
Popularity:	75.60%
Revised:	2005-06-07
Revisions:	6

Random Vectors and Joint Distributions (m23318)

Author: Paul E Pfeiffer

Keywords: applied probability, joint distribution, random variables, random vectors

Summary: Often we have more than one random variable. Each can be considered separately, but usually they have some probabilistic ties which must be taken into account when they are considered jointly. We treat the joint case by considering the individual random variables as coordinates of a random vector. We extend ... joint distribution.

Subject:	Mathematics and Statistics
Language:	English
Popularity:	77.36%
Revised:	2009-09-18
Revisions:	8

Random Vectors and MATLAB (m23320)

Author: Paul E Pfeiffer

Keywords: applied probability, matlab, m-procedures, probability, simple random variables

Summary: The systematic formulation in the previous module Minterms shows that each Boolean combination, as a union of minterms, can be designated by a vector of zero-one coefficients. A coefficient one in the ith position (numbering from zero) indicates the inclusion of minterm Mi in the union. We formulate this ... and solution.

Subject:	Mathematics and Statistics
Language:	English
Popularity:	87.67%
Revised:	2009-09-18
Revisions:	7

Range (m12381)

Author: Catherine Schmidt-Jones

Keywords: alto, baritone, bass, coloratura, contra, contrabass, contralto, countertenor, mezzo-soprano, piccolo, possible range, power range, practical range, range, soprano, tenor

Summary: Each type of voice and musical instrument has a characteristic pitch range.

Subject:	Arts
Language:	English
Popularity:	99.36%
Revised:	2013-02-15
Revisions:	11

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