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introduce Hawkes Process (HP) in statistics, not in other fields and find mean value and variance for HP with exponential self-exciting function, 2. state and prove the central limit theorem for the HP. Don’t write answers directly like mean and variance, please explain and prove how you get them. Attachment may be helpful, but please be focused on the statistical or mathematical field.
re critical to his theory regarding the scope of administrative prerogative, specifically concerning the complex politics of resistance. John Locke describes prerogative as the ‘power to act according to discretion, for the public good, without the prescription of the law, and sometimes even against it’; therefore stating that the executive is capable of taking actions that lie beyond the given legal framework of the constitution or written laws, in the case that their actions may advance the common good of the people, and of society as a whole. Ensuring their use for the advancement of the common good of the people and the understanding that prerogative powers are not imbued as a natural right, Locke emphasises that these powers are accompanied by the right to resist unlawful government by the people. It is for this reason that for many theorists, Locke is viewed more critically as the ‘origin of our contemporary tangle of lawless emergency governance’. Locke’s theory allows for governments, and executive bodies to step outside of the law in order to deal with public concern or emergency; “where the legislative and executive power are in distinct hands, (as they are in all moderated monarchies, and well-framed governments) there the good of the society requires that several things should be left to the discretion of him that has the executive power”; therefore one may show an understanding of prerogative as a liminal concept: occupying an “in-between” space for the legislature and the executive, it is this liminality that elucidates prerogative’s resilience. These tensions or ambiguities structure contemporary discussions of prerogative and, similarly primary literature focusing on emergency powers more broadly. Despite the emphasis placed on the executive as the primary body to carry out the motive principle of the given prerogative, one may argue in concordance with Lockean theory that the scope for such prerogative is at the behest of the infrastructure of the legislature, thus allowing for the body to play a key regulatory role. Henceforth, it must be taken into consideration that Locke refrains from calling prerogative executive power, rather Locke explicitly makes prerogative into a right of nature. In spite of Locke’s emphasis on the scope of prerogative right under an executive body, it may be said that such power is not an inherent right, therefore allowing the deliberative assemblies to close in on executive individuals through the use of authority to make laws for a political entity through the use of primary legislation. In this way the balance of power between the two branches of government allows one to maintain Locke’s theory, in contempt with the belief that such a system would endowing the executive with too much power relative to the legislature. However, it is critical that we consider the basis for Locke’s literature, as set in its given historical context; therefore in order to critically examine and thoroughly interpret Locke’s assessment of the scope o
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