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Degenerate distribution

In mathematics, a degenerate distribution is a probability distribution in a space with support only on a space of lower dimension. If the degenerate distribution is univariate it is a deterministic distribution and takes only a single value. Examples include rolling a die whose sides all show the same number; this distribution satisfies the definition of "random variable" though it does not appear random in the everyday sense of the word. In the case of a real-valued random variable, the degenerate distribution is localized at a point k0 on the real line; the probability mass function equals 1 at 0 elsewhere. The degenerate univariate distribution can be viewed as the limiting case of a continuous distribution whose variance goes to 0 causing the probability density function to be a delta function at k0, with infinite height there but area equal to 1; the cumulative distribution function of the univariate degenerate distribution is: F k 0 = { 1, if x ≥ k 0 0, if x < k 0 {\displaystyle F_=\left\ In probability theory, a constant random variable is a discrete random variable that takes a constant value, regardless of any event that occurs.

This is technically different from an surely constant random variable, which may take other values, but only on events with probability zero. Constant and surely constant random variables, which have a degenerate distribution, provide a way to deal with constant values in a probabilistic framework. Let X: Ω → R be a random variable defined on a probability space. X is an surely constant random variable if there exists k 0 ∈ R such that Pr = 1, is furthermore a constant random variable if X = k 0, ∀ ω ∈ Ω. Note that a constant random variable is surely constant, but not vice versa, since if X is surely constant there may exist γ ∈ Ω such that X ≠ k0. For practical purposes, the distinction between X being constant or surely constant is unimportant, since the cumulative distribution function F of X does not depend on whether X is constant or'merely' surely constant. In either case, F = { 1, x ≥ k 0, 0, x < k 0. The function F is a step function. Degeneracy of a multivariate distribution in n random variables arises when the support lies in a space of dimension less than n.

This occurs. For example, in the 2-variable case suppose that Y = aX + b for scalar random variables X and Y and scalar constants a ≠ 0 and b. All the possible points fall on the one-dimensional line y = ax + b. In general when one or more of n random variables are linearly determined by the others, if the covariance matrix exists its determinant is 0, so it is positive semi-definite but not positive definite, the joint probability distribution is degenerate. Degeneracy can occur with non-zero covariance. For example, when scalar X is symmetrically distributed about 0 and Y is given by Y = X 2, all possible points fall on the parabola y = x 2, a one-dimensional subset of the two-dimensional space

Light and Lively

Light and Lively is an album led by drummer Louis Hayes, recorded in 1989 and released on the Danish SteepleChase label. The Allmusic review called it "Another good one". "Light and Lively" – 12:27 "If You Could See Me Now" – 8:25 "Enchantment" – 6:13 "The 10th Dimension" – 11:57 Bonus track on CD "For the Love of What" – 6:21 "Darian" – 9:48 "Blues for Macao" – 10:26 Louis Hayes – drums Charles Tollivertrumpet Bobby Watson – alto saxophone Kenny Barronpiano Clint Houstonbass

Ian Rawcliffe

Ian Rawcliffe is a former President of the German Rugby Federation. He held this position from 1996 to 2004 and, from 2013 to 2015. Rawcliffe was born born 19 December 1948 in Burnley and came to Germany with the British Army in the 1970s. Since 1975 he has lived in Rödermark, near Frankfurt and is a member of BSC Offenbach, a club he coached in the 1980s. Rawcliffe first held the position of President of the German Rugby Federation from 1996 to 2004, when he stepped down for personal reasons and was succeeded by Bernd Leifheit, he became President for a second time in 2013, succeeding Ralph Götz and stepped down in July 2015 and was replaced by Klaus Blank. Deutscher Rugby-Verband - Official Site

Policy

A policy is a deliberate system of principles to guide decisions and achieve rational outcomes. A policy is a statement of intent, is implemented as a procedure or protocol. Policies are adopted by a governance body within an organization. Policies can assist in both objective decision making. Policies to assist in subjective decision making assist senior management with decisions that must be based on the relative merits of a number of factors, as a result are hard to test objectively, e.g. work-life balance policy. In contrast policies to assist in objective decision making are operational in nature and can be objectively tested, e.g. password policy. The term may apply to government, private sector groups, as well as individuals. Presidential executive orders, corporate privacy policies, parliamentary rules of order are all examples of policy. Policy differs from rules or law. While law can compel or prohibit behaviors, policy guides actions toward those that are most to achieve a desired outcome.

Policy or policy study may refer to the process of making important organizational decisions, including the identification of different alternatives such as programs or spending priorities, choosing among them on the basis of the impact they will have. Policies can be understood as political, managerial and administrative mechanisms arranged to reach explicit goals. In public corporate finance, a critical accounting policy is a policy for a firm/company or an industry, considered to have a notably high subjective element, that has a material impact on the financial statements; the intended effects of a policy vary according to the organization and the context in which they are made. Broadly, policies are instituted to avoid some negative effect, noticed in the organization, or to seek some positive benefit. Corporate purchasing policies provide an example of how organizations attempt to avoid negative effects. Many large companies have policies that all purchases above a certain value must be performed through a purchasing process.

By requiring this standard purchasing process through policy, the organization can limit waste and standardize the way purchasing is done. The State of California provides an example of benefit-seeking policy. In recent years, the numbers of hybrid cars in California has increased in part because of policy changes in Federal law that provided USD $1,500 in tax credits as well as the use of high-occupancy vehicle lanes to hybrid owners. In this case, the organization created an effect through policy. Policies have side effects or unintended consequences; because the environments that policies seek to influence or manipulate are complex adaptive systems, making a policy change can have counterintuitive results. For example, a government may make a policy decision to raise taxes, in hopes of increasing overall tax revenue. Depending on the size of the tax increase, this may have the overall effect of reducing tax revenue by causing capital flight or by creating a rate so high that citizens are deterred from earning the money, taxed.

The policy formulation process theoretically includes an attempt to assess as many areas of potential policy impact as possible, to lessen the chances that a given policy will have unexpected or unintended consequences. In political science, the policy cycle is a tool used for the analyzing of the development of a policy item, it can be referred to as a "stagist approach", "stages heuristic" or "stages approach". It is thus a rule of thumb rather than the actual reality of how policy is created, but has been influential in how political scientists looked at policy in general, it was developed as a theory from Harold Lasswell's work. Harold Lasswell's popular model of the policy cycle divided the process into seven distinct stages, asking questions of both how and they how public policies should be made. With the stages ranging from intelligence, prescription, application and appraisal, this process inherently attempts to combine policy implementation to formulated policy goals. One version by James E. Anderson, in his Public Policy-Making has the following stages: Agenda setting – The recognition of certain subject as a problem demanding further government attention.

Policy formulation – Involves exploring a variation of options or alternative courses of action available for addressing the problem. Decision-making – Government decides on an ultimate course of action, whether to perpetuate the policy status quo or alter it. Implementation – The ultimate decision made earlier will be put into practice. Evaluation – Assesses the effectiveness of a public policy in terms of its perceived intentions and results. Policy actors attempt to determine whether the course of action is a success or failure by examining its impact and outcomes. An eight step policy cycle is developed in detail in The Australian Policy Handbook by Peter Bridgman and Glyn Davis: Issue identification Policy analysis Consultation Policy instrument development Building coordination and coalitions Program Design: Decision making Policy Implementation Policy EvaluationThe Althaus, Bridgman & Davis model is

Jardine Libaire

Jardine Libaire is an American writer based in Austin, Texas. She is author of the novel White Fur. Jardine is a graduate of Skidmore College and a 1997 graduate of the University of Michigan Creative Writing MFA Program, where she was a winner of the Hopwood Award. Jardine has been the recipient of residency fellowships from the Edward F. Albee Foundation, the Ucross Foundation, the Saltonstall Foundation, Brush Creek Foundation for the Arts, OMI International Arts Center, she was a winner of the Glascock Poetry Prize. Jardine collaborated on the book Gravity is Stronger Here, contributing nonfiction poems that complement Phyllis B. Dooney's photographs of a family in Greenville, MS; this project won Honorable Mention for the 2016 Dorothea Lange - Paul Taylor Prize. Here Kitty Kitty ISBN 0-316-73688-0 White Fur ISBN 1-474-604-88-9 Miss Educated: An Upper Class Novel ISBN 0-06-085083-3 The Upper Class ISBN 0-06-085082-5 Crash Test ISBN 0-06-085085-X Off Campus ISBN 0-06-085084-1 Official website

Secrets and Lies (American TV series)

Secrets and Lies was an American mystery anthology television series that aired on ABC from March 1, 2015 to December 4, 2016. The series is based on the Australian television series of the same name, developed for American television by Barbie Kligman; the series follows Detective Andrea Cornell of the fictional Charlotte-Mecklenburg County Police Department as she investigates homicide cases. In the first season, Ben Crawford becomes the prime suspect in the death of a young boy who lived in his neighborhood. In the second season, Cornell investigates Eric Warner, a newly married heir to his family's private equity firm, when his wife Kate is murdered; the series was renewed for a second season on May 7, 2015, which premiered on September 25, 2016 and concluded on December 4, 2016. On May 11, 2017, ABC cancelled the series after two seasons. Ben Crawford is a self-employed contractor, married to Christy with whom he has two daughters, Natalie, 16, Abby, 12, his best friend, lives in their summer house.

They have a neighbor, estranged from her husband Scott, in the military. Jess and Scott have a five-year-old son named Tom. While out for an early morning run, Ben discovers Tom's body. Detective Cornell is convinced Ben is the killer, Ben cannot prove his innocence because he suffered a blackout after going out drinking with Dave following a fight with Christy over her suspicion of an affair with Jess; the Crawfords are shunned by the community. They learn that Tom was in fact Ben's son, the result of a one-night affair, only revealed to him after DNA tests by police. Ben conducts his own investigations, leading to false accusations against other neighbors, he is manipulated by a reporter, looking to take down Cornell, kidnapped by a neighbor, Kevin, a former CIA operative, who attempts to extract a confession through torture. The rift with Dave is repaired only after Dave confesses to spiking Ben's drink the night of the murder. Together they retrace Ben's steps. Cornell begins to consider other suspects.

By this time Ben's marriage has fallen apart. After sleeping with Jess once more, Ben discovers. Independently of each other and Ben discover the awful truth that Tom was killed by Abby, she confesses to her family that it was an accident, a failed plan to hide Tom for a short while to make it appear he was missing, to induce Scott to come home and prevent her father leaving Christy for Jess. Ben decides to confess to the murder to protect Abby, despite the protestations of Cornell, convinced Abby will kill again and vows to put her away. Abby reveals. In Season two, Ben is revealed to have been killed in jail. However, his innocence came to light afterwards; these facts have put a stain on Cornell's reputation as a detective. It is unknown as of yet whether or not Abby was revealed to be Tom's real killer or if she succeeded in evading justice. Eric Warner, a newly married heir to his family's private equity firm, is under suspicion from Detective Cornell when his wife Kate is murdered. Secrets and Lies was given its initial 10-episode series commitment in October 2013.

Barbie Kligman was brought in as executive producer and showrunner while the producers from the original series, Tracey Robertson and Nathan Mayfield, serve as executive producers. On May 9, 2014, Secrets and Lies was picked up by ABC to air as a mid-season entry during the 2014–15 season. An additional scene from the season 1 finale was made available online, set 14 months after the rest of the episode, with Natalie clearing Ben's name. Cornell: Confidential is a web series by ABC Studios and Disney/ABC Digital Media Studios which accompanies the television series; each webisode was released online after the television episode aired and gives additional clues told from the perspective of Detective Cornell. Secrets and Lies has received mixed criticism. On Rotten Tomatoes, it received a 36% approval rating, with a rating average of 4.7/10, based on 30 reviews. Its critical consensus reads: "While some may find its limited intrigue compelling and Lies is undone by wooden performances, excessive red herrings, bad scripts."

On Metacritic, it scored 48 out based on 22 "mixed or average" reviews. On March 16, 2015, ABC and the show's producers came under fire from the bleeding disorder community for portraying hemophilia as an incestuous disease with Michael Beach's character stating: "Hemophilia is the nasty byproduct of incest." A petition for a public apology was started on Change.org. In subsequent airings of the episode, the line was removed; the series premiered in Germany on Universal Channel on March 10, 2015. The second season aired from June 20 to August 22, 2016; the series premiered in India on Zee Café on April 11, 2015. The series premiered in France on M6 on November 5, 2015; the series premiered in Turkey on Dizimax Drama. The series premiered in Brazil on Globo on October 17, 2016; the series premiered in Italy on Rai 4 on September 13, 2015. Official website Secrets and Lies on IMDb