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Topic: Discrete probability distribution

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	Probability
		Probability applications include even more than Statistics, which is usually based on the idea of probability distributions and the Central limit theorem.
		There are several important, discrete distributions, such as the discrete uniform distribution, the Poisson distribution, the binomial distribution, the negative binomial distribution and the Maxwell-Boltzmann distribution.
		Governments typically apply probability methods in environment regulation[?] where it is called "pathway analysis[?]", and are often measuring well-being using methods that are stochastic in nature, and choosing projects to undertake based on their perceived probable impact on the population as a whole, statistically.
	www.ebroadcast.com.au /lookup/encyclopedia/pr/Probability.html (1522 words)

	STA-2122
		Probability Histogram is a bar graph associated with a discrete probability distribution.
		Probability Point Graph is a graphical representation of a probability distribution associating the heights of vertical lines with the given probabilities.
		Parameters of the binomial probability distribution are the number of trials “n” and the rate of success “p” (probability of success for each trial).
	www.fiu.edu /~gomezra/Vocab4-8.htm (925 words)

	Discrete Probability Distribution - BERNOULLI DISTRIBUTION (Site not responding. Last check: 2007-10-09)
		A random variable X has a Bernoulli distribution with parameter p if it can assume a value of 1 with a probability of p and the value of 0 with a probability of (1-p).
		The mean of a random variable X that has a Bernoulli distribution with parameter p is
		A random variable whose value represents the outcome of a coin toss (1 for heads, 0 for tails, or vice-versa) is a Bernoulli variable with parameter p, where p is the probability that the outcome corresponding to the value 1 occurs.
	library.advanced.org /10030/6dpdbd.htm (128 words)

	Statistics Glossary - random variables and probability distributions
		Discrete case : When a die is thrown, each of the possible faces 1, 2, 3, 4, 5, 6 (the xi's) has a probability of 1/6 (the p(xi)'s) of showing.
		Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten.
		The Geometric distribution is related to the Binomial distribution in that both are based on independent trials in which the probability of success is constant and equal to p.
	www.stats.gla.ac.uk /steps/glossary/probability_distributions.html (2101 words)

	[No title]
		Chapter 11, "Probability Meets Data," introduced the sample sum of random draws with replacement from a box of tickets, each of which is labeled "0" or "1." The sample sum is a random variable, and its probability distribution, the binomial distribution, is a discrete probability distribution.
		For discrete probability distributions, the number of values that have nonzero probability is countable.
		Even though the random variable X counts "successes" in a fixed number (four) of independent trials, it does not have a binomial probability distribution, because the probability of success is not the same in every trial: It is 1/2 in the trials that involve the coin, and 1/6 in the trials that involve the die.
	www.stat.berkeley.edu /users/stark/SticiGui/Text/ch12.htm (5742 words)

	1.3.6.1. What is a Probability Distribution
		Since continuous probability functions are defined for an infinite number of points over a continuous interval, the probability at a single point is always zero.
		The property that the integral must equal one is equivalent to the property for discrete distributions that the sum of all the probabilities must equal one.
		Discrete probability functions are referred to as probability mass functions and continuous probability functions are referred to as probability density functions.
	www.itl.nist.gov /div898/handbook/eda/section3/eda361.htm (384 words)

	math lessons - Information entropy
		Thus, the entropy of the source alphabet, with its given empiric probability distribution, is a number equal to the number (possibly fractional) of symbols of the "ideal alphabet", with an optimal probability distribution, necessary to encode for each symbol of the source alphabet.
		Also note that "optimal probability distribution" here means a uniform distribution: a source alphabet with n symbols has the highest possible entropy (for an alphabet with n symbols) when the probability distribution of the alphabet is uniform.
		The entropy of the distribution is obtained from the logarithm of Ω:
	www.mathdaily.com /lessons/Information_entropy (1401 words)

	Discrete probability (Site not responding. Last check: 2007-10-09)
		A probability distribution table is simply a listing of each potential value of the random variable along with its probability.
		The probability distribution of the outcomes of the number of girls in 3 child families is: (don't worry where these numbers come from):
		Probability functions can be drawn as a graph by simply placing a bar or spike above each value to represent the probability of the event.
	www.math.sfu.ca /~cschwarz/Stat-301/Handouts/node63.html (277 words)

	[No title]
		This is referred to as count data and is another example of the distribution of a discrete random variable.
		The Binomial Distribution and the Poisson Distribution are examples of distributions of discrete random variables.
		The change in the probability from trial to trial becomes smaller as the population size increases relative to the size of the sample.
	www.shsu.edu /~mgt_ves/BAN530/DiscreteProbDistNOTES.doc (598 words)

	Lecture Notes 5
		A probability distribution is similar to the frequency distribution of a quantitative population because both provide a long-run frequency for outcomes.
		The poisson probability distribution provides a close approximation to the binomial probability distribution when n is large and p is quite small or quite large.
		The hypergeometric distribution is used to determine the probability of a specified number of successes and/or failures when (1) a sample is selected from a finite population without replacement and/or (2) when the sample size, n, is greater than or equal to 5% of the population size, N, i.e., [ n>=5% N].
	business.clayton.edu /arjomand/business/l5.html (1466 words)

	GBS 221 Class Notes 6 (Site not responding. Last check: 2007-10-09)
		A discrete random variable is a numerical outcome of an experiment that assumes either a finite number of values or an infinite sequence of values.
		A discrete probability distribution is a complete list of discrete random variables and their associated probability.
		A poisson probability distribution is useful for experiments estimating the number of occurrences over a specified time/space.
	www.sc.maricopa.edu /people/sandblom/221notes6.html (348 words)

	Discrete Probability Distribution at blacksacademy.co.uk
		Experimentally, a probability is determined by the ratio of the number of times....
		The theoretical values of the mean and variance are calculated from the theoretical probability distribution.
		The theoretical values of a discrete probability distribution are usually presented in the form of a table: [Diagram goes here - download the pdf article for the diagram.} It is from such a table that the theoretical, expected mean and variance are calculated.
	www.blacks.veriovps.co.uk /content/3194.html (296 words)

	Discrete probability distribution - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab1.cs.virginia.edu) (Site not responding. Last check: 2007-10-09)
		If a random variable is discrete, then the set of all values that it can assume with nonzero probability is finite or countably infinite, because the sum of uncountably many positive real numbers (which is the smallest upper bound of the set of all finite partial sums) always diverges to infinity.
		In the cases most often considered, this set of possible values is a topologically discrete set in the sense that all its points are isolated points.
		The Poisson distribution, the Bernoulli distribution, the binomial distribution, the geometric distribution, and the negative binomial distribution are among the most well-known discrete probability distributions.
	en.wikipedia.org.cob-web.org:8888 /wiki/Discrete_probability_distribution (371 words)

	soci208 - module 6 (Site not responding. Last check: 2007-10-09)
		The probability distribution of a Bernouilli RV B is shown in Table 2.
		Example: reconstruct the probability distribution for the binomial p=0.2, n=3 shown in NWW Figure 7.3 (a) p.
		It will be shown later that as n increases the binomial distribution tends to a normal distribution; the convergence is faster when p is close to.5, slower when p is either close to 0 or close to 1.
	www.unc.edu /~nielsen/soci208/m6/m6.htm (801 words)

	www.com - Discrete probability distribution (Site not responding. Last check: 2007-10-09)
		In mathematics, a probability distribution is called discrete, if it is fully characterized by a probability mass function.
		In the cases most often considered, this set of possible values is a topologically discrete set in the sense that all its points are isolated point s.
		Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf) increases only by jump discontinuity — that is, its cdf increases only where it "jumps" to a higher value, and is constant between those jumps.
	willpay.info /6366 (323 words)

	Discrete Probability Distribution Homework 1 (Site not responding. Last check: 2007-10-09)
		Below is a probability density function for a random variable X where X represents the number of failures in 5 attempts to graft an orange tree root.
		Probabilities must add to 1, so f(5) is.01.
		Below is a probability density function for a random variable X which counts the number of holes a certain type drill bit can drill in rock before breaking.
	science.kennesaw.edu /~mbell/DiscreteHW1key.html (313 words)

	Probability
		In this case, the distributions are constructed by counting the number of times each element of the sample space occur in a large series of experiments.
		In general, however, the probability distribution of the i’th event might depend on many of the events that precede it.
		In general, we will always be trying to balance a tradeoff between the accuracy to which a probability distribution can model the phenomena versus the amount of data we would require to adequately estimate it.
	www.cs.rochester.edu /u/james/CSC248/lecture2.htm (2968 words)

	mappda.info - Discrete probability distribution (Site not responding. Last check: 2007-10-09)
		In matℎematics, a probability distribution is called discrete, iƒ it is ƒully cℎaracterized by a probability mass ƒunction.
		Tℎe Poisson distribution, tℎe Bernoulli distribution, tℎe binomial distribution, tℎe geometric distribution, and tℎe negative binomial distribution are among tℎe most well-known discrete probability distributions.
		Equivalently to tℎe above, a discrete random variable can be deƒined as a random variable wℎose cumulative distribution ƒunction (cdƒ) increases only by jump discontinuity &mdasℎ; tℎat is, its cdƒ increases only wℎere it "jumps" to a ℎigℎer value, and is constant between tℎose jumps.
	mappda.info /6366 (420 words)

	Discrete Distributions Practice Quiz
		The mean of a general discrete random variable is equal to the sample mean, xbar.
		The mean of any discrete probability distribution includes individual x values and
		Any copying, distribution, or preparation of derivative works is strictly prohibited.
	jan.ucc.nau.edu /quizserver/pinto/discrete1.html (155 words)

	Discrete Particle Distribution Model for Advection-Diffusion Transport (Site not responding. Last check: 2007-10-09)
		A new methodology, named DisPar, based on a discrete probability distribution for a particle displacement, was developed to solve 1D advection-diffusion transport problems in water bodies.
		The discrete probability distribution for the particle displacement was developed as an average and variance function.
		These probabilities were used to predict the deterministic mass transfer between cells in one time step, and therefore the particle concentration in each cell was considered the state variable.
	www.pubs.asce.org /WWWdisplay.cgi?0002345 (211 words)

	MTH 160 - Monroe Community College Web Site
		1.9 Describe the characteristics of the distributions: normal, uniform or rectangular, skewed, and bimodal.
		5.4 Explain that the parameters of the binomial distribution are n and p and that the possible values of the binomial random variable are the integers from zero to n, inclusive.
		6.4 Demonstrate that area, proportion of population, and probability are equivalent notions for continuous probability distributions.
	www.monroecc.edu /depts/math/mth160.htm (963 words)

	Discrete Probability Distributions (Site not responding. Last check: 2007-10-09)
		The result of this process is called a discrete probability distribution.
		The above table is an example of a discrete probability distribution.
		A probability distribution may be displayed as a relative frequency histogram.
	home.xnet.com /~fidler/triton/math/review/mat170/probty/p-dist/discrete/discrt1.htm (325 words)

	CiteULike: Approximate Discrete Probability Distribution Representation using a Multi-Resolution Binary Tree (Site not responding. Last check: 2007-10-09)
		The problem of efficient representation of probability distributions is central in term of computational efficiency in the field of probabilistic reasoning.
		The other advantages of our approach are the ability to refine dynamically the distribution every time it is needed leading to a more accurate representation of the probability distribution and to an anytime representation of the distribution.
		The main problem arises when dealing with joint probability distributions over a set of random variables: they are always represented using huge probability arrays.
	www.citeulike.org /user/gane5h/article/635165 (395 words)

	[No title]
		From the definition of a random variable, X as defined in this experiment, is a random variable.¡2yêþó ¨Probability Distributionsª ó¨-Characteristics of a Probability Distribution¡.- ¨uThe probability of an outcome must always be between 0 and 1.
		Examples: Height of a basketball player, the length of a nap.¡&§yêþó ¨/The Mean of a Discrete Probability Distribution¡0/¨ÑThe mean: reports the central location of the data.
		The variance of a discrete distribution is denoted by the Greek letter (sigma squared).
	www.iit.edu /~abdemet/CH5.PPT (547 words)

	The Binomial Distribution (Site not responding. Last check: 2007-10-09)
		Perhaps the most commonly used discrete probability distribution is the binomial distribution.
		The random variable X of a binomial distribution counts the number of successes in n trials.
		The probability that X is a certain value x is given by the formula
	stat.tamu.edu /stat30x/notes/node66.html (243 words)

	Discrete Probability Distributions
		Calculate the mean, variance, and standard deviation of a discrete probability distribution.
		Describe the characteristics of and compute probabilities using the binomial probability distribution.
		Describe the characteristics of and compute probabilities using the Poisson probability distribution.
	highered.mcgraw-hill.com /sites/0072983965/student_view0/chapter6 (172 words)

	[No title]
		¡jª- ó%U¨Discrete - Features¨¡The sum of the probabilities of the various outcomes is 1.00.
		The probability of a particular outcome is between 0 and 1.00.
		From the definition of a random variable, x as defined in this experiment, is a random variable.¡ó ;¨Discrete PD - The Mean Reports the central location of the data. The long-run average value of the random variable. Also referred to as its expected value E(X) in a probability distribution Is a weighted average¡`3'#3'#ó
	www.csulb.edu /~asafer/math480/stat_chpt1/MA211-Chp6Lecture.ppt (868 words)

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