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# Topic: Probability mass function

###### In the News (Tue 23 Jul 19)

 [No title] Function: Returns probability mass function and the cumulative distribution function of the binomial distribution b(n,p). Plots the probability density function, the cumulative ditribution function, and user-specified percentiles. Function: Returns probability mass function and the cumulative distribution function of the discrete uniform distribution on first m positive integers. homepage.mac.com /samchops/ROTHMAN/COURSES/STA342/S2006/matlab.html   (1164 words)

 Probability mass function - Wikipedia, the free encyclopedia A probability mass function differs from a probability density function in that the values of the latter, defined only for continuous random variables, are not probabilities; rather, its integral over a set of possible values of the random variable is a probability. The discontinuity of probability mass functions reflects the fact that the cumulative distribution function of a discrete random variable is also discontinuous. Probability mass functions may also be defined for any discrete random variable, including constant, binomial (including Bernoulli), negative binomial, Poisson, geometric and hypergeometric random variables. en.wikipedia.org /wiki/Probability_mass_function   (284 words)

 Statistics Glossary - Probability Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1. For a continuous random variable, the cumulative distribution function is the integral of its probability density function. The probability density function of a continuous random variable is a function which can be integrated to obtain the probability that the random variable takes a value in a given interval. www.cas.lancs.ac.uk /glossary_v1.1/prob.html   (3540 words)

 Probability density function   (Site not responding. Last check: 2007-10-18) In mathematics, a probability density function (pdf) serves to represent a probability distribution in terms of integrals. Any function that is everywhere non-negative and whose integral from −∞ to +∞ is equal to 1 is a Probability density function. Not every Probability distribution has a density function: the distributions of discrete random variables do not; nor does the Cantor distribution, even though it has no discrete component, i.e., does Not assign positive Probability to any individual point. probability-density-function.iqnaut.net   (447 words)

 Probability 101 A probability measure is a function that defines the probability of all different events. In probability, the relative frequency of certain events is known for a population and we ask for the probability of events for a subset of this population. In probability, a subset of the population would be a set of samples and called an event. www.cs.cornell.edu /Courses/CS664/1997sp/probability.htm   (1188 words)

 STATS 241.3 What to know You should know the meaning of probability mass function (pmf) and cumulative distribution function (cdf) (which are called just "probability function" and "distribution function" in the book) for discrete random variables. You should be able to draw and interpret probability histograms, and to recognize that an expected value lies at the centre of gravity of the probability histogram. You should know that the moment generating function of the sum of independent random variables is given by the product of their moment generating functions. math.usask.ca /~bickis/courses/stats241/syllabus.html   (943 words)

 1.3.6.6.18. Binomial Distribution   (Site not responding. Last check: 2007-10-18) The binomial distribution is used to obtain the probability of observing x successes in N trials, with the probability of success on a single trial denoted by p. The following is the plot of the binomial cumulative distribution function with the same values of p as the pdf plots above. Note that because this is a discrete distribution that is only defined for integer values of x, the percent point function is not smooth in the way the percent point function typically is for a continuous distribution. www.itl.nist.gov /div898/handbook/eda/section3/eda366i.htm   (235 words)

 StatPrimer 4A Exercises - © B. Gerstman The attending physician tells the patient that the probability of survival is 80%. Explain the meaning of the probability estimate to the patient in terms he or she will understand. (A) Use statistical notation to identify the probability mass function that describes the number of asthmatics in a random sample. www.sjsu.edu /faculty/gerstman/StatPrimer/probability-bin.htm   (1035 words)

 Probability density function - Wikipedia, the free encyclopedia (via CobWeb/3.1 planet2.scs.cs.nyu.edu)   (Site not responding. Last check: 2007-10-18) A probability density function is non-negative everywhere and its integral from −∞ to +∞ is equal to 1. In the field of statistical physics, a non-formal reformulation of the relation above between the derivative of the cumulative distribution function and the probability density function is generally used as the definition of the probability density function. If the probability density function of an independent random variable x is given as f(x), it is possible to calculate the probability density function of some variable y which depends on x. en.wikipedia.org.cob-web.org:8888 /wiki/Probability_density_function   (986 words)

 Probability-generating function - Wikipedia, the free encyclopedia In probability theory, the probability-generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. The probability-generating function of a negative binomial random variable, the number of trials required to obtain the rth success with probability of success in each trial p, is The probability-generating function is occasionally called the z-transform of the probability mass function. en.wikipedia.org /wiki/Probability-generating_function   (635 words)

 No Title   (Site not responding. Last check: 2007-10-18) As we have seen, not all distribution functions are continuous. In fact, the distribution function of a discrete random variable has a jump discontinuity at every point where the probability mass function is not 0, and the size of the jump is the value of the probability mass function. Thus a random variable has a continuous distribution if and only if its probability mass function is always 0. www.uwm.edu /~ericskey/361material/361F98/L09/index.html   (360 words)

 BINOMDIST   (Site not responding. Last check: 2007-10-18) For example, BINOMDIST can calculate the probability that two of the next three babies born are male. Cumulative   is a logical value that determines the form of the function. If cumulative is TRUE, then BINOMDIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are exactly number_s successes. www.nv.doe.gov /_vti_bin/help/1033/sts/html/lbinomdi.htm   (197 words)

 Probability and Statistics   (Site not responding. Last check: 2007-10-18) Probability and Statistics are not one and the same. Probability can be viewed either as the long-run frequency of occurrence or as a measure of the plausibility of an event given incomplete knowledge - but not both. Statistics are functions of the observations (data) that often have useful and even surprising properties. www.statisticalengineering.com /probability_and_statistics.htm   (452 words)

 Random Variables This activity is intended to clarify the relationship between discrete sample spaces, discrete random variables, probability mass functions, and cumulative distribution functions, with a focus on computing probabilities using these concepts. The real importance of the cumulative distribution and probability mass function is their ability to describe the behavior of a population from a plot of sample data. A function whose domain is a sample space and whose range is a subset of the real numbers. www.saintmarys.edu /~psmith/345act7.html   (484 words)

 Probability - Sample Tests and Resources Know the "formal definitions" of Probability, conditional probability, mutually independent events, random variable, and the probability mass function of a random variable. Finally, be able to compute using enumeration techniques and apply them to probabilities and random variables, as, for example done in the assigned homework. Be able to compute the moments and moment generating functions for these random variables (both continuous and discrete). www.math.sc.edu /~sharpley/math511/SampleTests.html   (457 words)

 Lecture 4—Wednesday, January 18, 2006 The probability of observing two or more events in an interval, when the interval in question is very small, is approximately zero. The probability mass function of the negative binomial distribution comes in two distinct versions. Since the probability of a success is a constant p on each of these trials, we're back in the binomial probability setting where the number of trials is x + r – 1. www.unc.edu /courses/2006spring/ecol/145/001/docs/lectures/lecture4.htm   (1355 words)

 No Title   (Site not responding. Last check: 2007-10-18) If a random phenomenon has m outcomes, each with probability 1/m, and if E is any event consisting of k of those outcomes, then P(E)=k/m. If the probability a transformer fails within one year is 0.008, approximate the probability fewer than three of the transformers fail within one year. All probabilities from any normal distribution can be reduced to probabilities from a standard normal (i.e. www.math.wpi.edu /Course_Materials/MA2611E98/lect4   (1419 words)

 [No title] That is, for any probability mass function that extends to infinity, the probabilities of possible values will tend to (but never reach) zero. The second way to evaluate probability mass functions is to compute them from the formula for a probability mass function (or density for continuous distributions). Plotting Probability Density Functions Plotting a probability density function for a continuous random variable follows much the same routine as does plotting a probability mass function for a discrete random variable. www.public.iastate.edu /~mskaiser/Stat341/rhandout2.doc   (2009 words)

 Probability Mass Functions   (Site not responding. Last check: 2007-10-18) distribution describes the probability of events; a PMF describes the `probability ``mass'' of numbers, values of an RV. Everywhere else the function is zero; the RV can't take values between these spikes. The sum of all probability masses must be exactly one. hci.ucsd.edu /14/spring02/node17.html   (252 words)

 AMS 311 The probability of a rectangular region is given by The random variables X and Y are jointly continuous if there exists a function f(x,y) defined for all real x and y, having the property that for very set C of pairs of real numbers (that is, C is a set in the two-dimensional plane) (c) Compute the probability that D, the distance from the origin of the point selected, is less than or equal to a. www.ams.sunysb.edu /~dorothy/handout20.html   (480 words)

 Using Matlab to visualize discrete joint probability mass functions     (Site not responding. Last check: 2007-10-18) A common example in a first course in probability involves rolling a pair of fair dice and the finding joint probability mass function associated with random variables X and Y, where X is the smaller outcome and Y is the larger outcome on the dice. which displays a representation of the space of random variables X and Y, along with the joint probability mass function and the marginal probability mass functions. The marginal probability mass functions of Y and X are computed as follows homepage.mac.com /samchops/B733177502/C1517039664/E20051111080333   (627 words)

 Chapters 3-4 Constructing a Probability Mass Function with EXCEL   (Site not responding. Last check: 2007-10-18) Assuming 60 percent of those caught lose their entire take and 40 percent lose half, graph the probability mass function using EXCEL. : Construction of the probability mass function for bank robberies first requires the defining of the random variable x, bank robbery take. The associated probabilities for these x values are 0.15 (= 1- 0.85), 0.34 (= 0.85×0.4), and 0.51 (= 0.85×0.6) After entering the x values in cells A1, A2 and A3 and the associated probabilities in B1, B2, and B3, the following steps lead to the probability mass function: www.indiana.edu /~iustats/query/chap3.htm   (423 words)

 1.3.6.6.19. Poisson Distribution   (Site not responding. Last check: 2007-10-18) The Poisson distribution is used to model the number of events occurring within a given time interval. The following is the plot of the Poisson probability density function for four values of Most general purpose statistical software programs, including Dataplot, support at least some of the probability functions for the Poisson distribution. www.itl.nist.gov /div898/handbook/eda/section3/eda366j.htm   (175 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. This probability density function (p.d.f.) is a symmetrical, bell-shaped curve, centred at its expected value µ. , if its probability density function is constant within a finite interval [a,b], and zero outside this interval (with a less than or equal to b). www.stats.gla.ac.uk /steps/glossary/probability_distributions.html   (2101 words)

 [No title] Discrete Case: Properties of a probability mass function (discrete probability distribution). Find the probability distribution Discrete Case: Cumulative Distribution In many instances we are interested in finding the probability of the observed value less than or equal some number. Their joint probability distribution is given as: f(x,y)x123Y10.050.050.1020.050.100.35300.200.10 Find the marginal distributions of x and y Find P(Y=3X=2) Find P(Y=3). www.stat.sc.edu /~quiton/courses/509/Sec03.doc   (1200 words)

 [No title]   (Site not responding. Last check: 2007-10-18) 0ò3ó ¨,Example for joint probability mass function ¡--¨=Consider the following table: Using the table, we have¡>>ó ~Joint and marginal distribution functions for continuous r.v. s¡@@ª9¨ Random variables X and Y are jointly continuous if there exists a function f(x, y) such that for every well-behaved subset C of lR2. X and Y are independent.¡0i÷jª Eó"¨\$Sums of independent random variables¡%%¨HSuppose that X and Y are independent continuous random variables having probability density functions fX and fY. Suppose p(x, y), the joint probability mass function of X and Y, is given by: What is Solution. home.att.net /~michael.engquist/ProbChap6.ppt   (566 words)

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