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01 May 15
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Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution
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14 Dec 14
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- Mode: for a discrete random variable, the value with highest probability (the location at which the probability mass function has its peak); for a continuous random variable, the location at which the probability density function has its peak.
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- Expected value or mean: the weighted average of the possible values, using their probabilities as their weights; or the continuous analog thereof.
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29 Apr 14
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of the possible outcomes of a random
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Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution can be specified by a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a probability density function.
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. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution can be specified by a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a probability density function.
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Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution can be specified by a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a probability density function.
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A probability distribution can either be univariate or multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector—a set of two or more random variables
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In the discrete case, one can easily assign a probability to each possible value: for example, when throwing a fair die, each of the six values 1 to 6 has the probability 1/6. In contrast, when a random variable takes values from a continuum, probabilities can be nonzero only if they refer to intervals: in quality control one might demand that the probability of a "500 g" package containing between 490 g and 510 g should be no less than 98%.
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- Mode: for a discrete random variable, the value with highest probability (the location at which the probability mass function has its peak); for a continuous random variable, the location at which the probability density function has its peak.
- Support: the smallest closed set whose complement has probability zero.
- Head: the range of values where the pmf or pdf is relatively high.
- Tail: the complement of the head within the support; the large set of values where the pmf or pdf is relatively low.
- Expected value or mean: the weighted average of the possible values, using their probabilities as their weights; or the continuous analog thereof.
- Median: the value such that the set of values less than the median has a probability of one-half.
- Variance: the second moment of the pmf or pdf about the mean; an important measure of the dispersion of the distribution.
- Standard deviation: the square root of the variance, and hence another measure of dispersion.
- Symmetry: a property of some distributions in which the portion of the distribution to the left of a specific value is a mirror image of the portion to its right.
- Skewness: a measure of the extent to which a pmf or pdf "leans" to one side of its mean.
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09 Mar 14
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distribution
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the most well-known
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Poisson distribution, the Bernoulli distribution, the binomial distribution, the geometric distribution, and the negative binomial distribution.
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07 Dec 12
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probability density function: a non-negative Lebesgue integrable function
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11 Jul 12
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09 Jul 12
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08 Jul 12
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03 Jul 12
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04 Jun 12
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In the discrete case, one can easily assign a probability to each possible value
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30 Mar 12
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21 Feb 12
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Discrete probability distribution for the sum of two dice.
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05 Sep 11
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03 Sep 11
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- Probability mass, Probability mass function, p.m.f.: for discrete random variables.
- Categorical distribution: for discrete random variables with a finite set of values.
- Probability density, Probability density function, p.d.f: Most often reserved for continuous random variables.
- Probability distribution function: Continuous or discrete, non-cumulative or cumulative.
- Probability function: Even more ambiguous, can mean any of the above, or anything else.
- Probability distribution: Either the same as probability distribution function. Or understood as something more fundamental underlying an actual mass or density function
As probability theory is used in quite diverse applications, terminology is not uniform and sometimes confusing. The following terms are used for non-cumulative probability distribution functions:
The following terms are somewhat ambiguous as they can refer to non-cumulative or cumulative distributions, depending on authors' preferences:
Finally,
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16 Apr 11
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describes the probability of a random variable taking certain values
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a function
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easily assign a probability
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values from a continuum
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refer to finite intervals
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describes the range of possible values that a random variable can attain
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spread or variability in almost any value that can be measured in a population
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. The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve"
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18 Nov 10
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16 Nov 10
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18 Oct 10
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05 May 09
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probability of each value
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within a particular interval
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probability distribution Pr
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function f
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05 Jun 08
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24 Apr 08
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A probability distribution describes the values and probabilities that a random event can take place. The values must cover all of the possible outcomes of the event, while the total probabilities must sum to exactly 1,
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The integral of the probability density function (pdf) over the entire area of the dartboard (and, perhaps, the wall surrounding it) must be equal to 1, since each dart must land somewhere.
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14 Apr 08
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02 Mar 08
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manipulations
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23 Jul 07
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27 Mar 07
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23 Jan 07
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31 Aug 06
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