Probability

Statistician A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects. Nature of the work[edit] According to the United States Bureau of Labor Statistics, as of 2010, 25,100 jobs were classified as statistician in the United States.[1] Of these people, approximately 30 percent worked for governments (federal, state, or local). Most employment as a statistician requires a minimum of a masters degree in statistics or a related field. See also[edit] List of statisticians References[edit] External links[edit]

Geometric distribution In probability theory and statistics, the geometric distribution is either of two discrete probability distributions: The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...}The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... } Which of these one calls "the" geometric distribution is a matter of convention and convenience. These two different geometric distributions should not be confused with each other. It’s the probability that the first occurrence of success require k number of independent trials, each with success probability p. for k = 1, 2, 3, .... The above form of geometric distribution is used for modeling the number of trials until the first success. for k = 0, 1, 2, 3, .... In either case, the sequence of probabilities is a geometric sequence. Moments and cumulants[edit] Let μ = (1 − p)/p be the expected value of Y. [citation needed]

Statistics Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.[1] It deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.[1] When analyzing data, it is possible to use one or both of statistics methodologies: descriptive and inferential statistics in the analysis data.[2] Scope[edit] Statistics is described as a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data,[3] or as a branch of mathematics[4] concerned with collecting and interpreting data. Statisticians improve data quality by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting the use of data through statistical models. Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences, government, and business. History[edit]

Binomial distribution Binomial distribution for with n and k as in Pascal's triangle The probability that a ball in a Galton box with 8 layers (n = 8) ends up in the central bin (k = 4) is In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Specification[edit] Probability mass function[edit] In general, if the random variable X follows the binomial distribution with parameters n and p, we write X ~ B(n, p). for k = 0, 1, 2, ..., n, where is the binomial coefficient, hence the name of the distribution. different ways of distributing k successes in a sequence of n trials. In creating reference tables for binomial distribution probability, usually the table is filled in up to n/2 values. Looking at the expression ƒ(k, n, p) as a function of k, there is a k value that maximizes it. and comparing it to 1. Recurrence relation where Example[edit]

Caret The caret and circumflex are not to be confused with other chevron-shaped characters, such as U+028C ʌ latin letter turned v or U+2227 ∧ logical and, which may occasionally be called carets too.[5][6] Origins[edit] Proofreading mark[edit] The caret was originally used, and continues to be, in handwritten form as a proofreading mark to indicate where a punctuation mark, word, or phrase should be inserted in a document.[7] The term comes from the Latin caret, "it lacks", from carēre, "to lack; to be separated from; to be free from".[8] The caret symbol is written below the line of text for a line-level punctuation mark such as a comma, or above the line as an inverted caret (cf. U+02C7 ˇ caron) for a higher character such as an apostrophe;[9] the material to be inserted may be placed inside the caret, in the margin, or above the line. Circumflex accent[edit] As regards computer systems, the original 1963 version of the ASCII standard reserved the code point 5Ehex for an up-arrow (↑).

Poisson distribution Discrete probability distribution Under a Poisson distribution with the expectation of λ events in a given interval, the probability of k events in the same interval is:[2]: 60 For instance, consider a call center which receives, randomly, an average of λ = 3 calls per minute at all times of day. If the calls are independent, receiving one does not change the probability of when the next one will arrive. Under these assumptions, the number k of calls received during any minute has a Poisson probability distribution. Receiving k = 1 to 4 calls then has a probability of about 0.77, while receiving 0 or at least 5 calls has a probability of about 0.23. Another example for which the Poisson distribution is a useful model is the number of radioactive decay events during a fixed observation period. History[edit] Definitions[edit] Probability mass function[edit] A discrete random variable X is said to have a Poisson distribution, with parameter if it has a probability mass function given by:[2]: 60 If

Linear regression In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted,[citation needed] rather than a single scalar variable.) In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. Linear regression has many practical uses. If the goal is prediction, or forecasting, or reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. where Example.

Poisson process In probability theory, a Poisson process is a stochastic process that counts the number of events[note 1] and the time that these events occur in a given time interval. The time between each pair of consecutive events has an exponential distribution with parameter λ and each of these inter-arrival times is assumed to be independent of other inter-arrival times. The process is named after the French mathematician Siméon Denis Poisson and is a good model of radioactive decay,[1] telephone calls[2] and requests for a particular document on a web server,[3] among many other phenomena. The Poisson process is a continuous-time process; the sum of a Bernoulli process can be thought of as its discrete-time counterpart. Definition[edit] The basic form of Poisson process, often referred to simply as "the Poisson process", is a continuous-time counting process {N(t), t ≥ 0} that possesses the following properties: Consequences of this definition include: Types[edit] Homogeneous[edit] Spatial[edit] . .