[FREE] 1998 Ap Statistics Free Response Answers
William H. Jefferys and James O. Berger generalize and quantify the original formulation's "assumptions" concept as the degree to which a proposition is unnecessarily accommodating to possible observable data. The model they propose balances the precision of a theory's predictions against their sharpness, preferring theories that sharply make correct predictions over theories that accommodate a wide range of other possible results. This, again, reflects the mathematical relationship between key concepts in Bayesian inference namely marginal probability , conditional probability , and posterior probability. The bias—variance tradeoff is a framework that incorporates the Occam's razor principle in its balance between overfitting i. Our preference for simplicity may be justified by its falsifiability criterion: we prefer simpler theories to more complex ones "because their empirical content is greater; and because they are better testable".
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Since it is absurd to have no logical method for settling on one hypothesis amongst an infinite number of equally data-compliant hypotheses, we should choose the simplest theory: "Either science is irrational [in the way it judges theories and predictions probable] or the principle of simplicity is a fundamental synthetic a priori truth. That is the meaning of Occam's Razor. They must both possess the same logical mathematical multiplicity cf. Hertz's Mechanics, on Dynamic Models. It simply says that unnecessary elements in a symbolism mean nothing. Signs which serve one purpose are logically equivalent; signs which serve no purpose are logically meaningless. Future positions of the sun, moon and other solar system bodies can be calculated using a geocentric model the earth is at the centre or using a heliocentric model the sun is at the centre.
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Both work, but the geocentric model arrives at the same conclusions through a much more complex system of calculations than the heliocentric model. This was pointed out in a preface to Copernicus ' first edition of De revolutionibus orbium coelestium. In science , Occam's razor is used as a heuristic to guide scientists in developing theoretical models rather than as an arbiter between published models. An often-quoted version of this constraint which cannot be verified as posited by Einstein himself [51] says "Everything should be kept as simple as possible, but not simpler. However, science has shown repeatedly that future data often support more complex theories than do existing data. Science prefers the simplest explanation that is consistent with the data available at a given time, but the simplest explanation may be ruled out as new data become available.
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Several background assumptions are required for parsimony to connect with plausibility in a particular research problem. It is a mistake to think that there is a single global principle that spans diverse subject matter. There is little empirical evidence that the world is actually simple or that simple accounts are more likely to be true than complex ones. For example, Max Planck interpolated between the Wien and Jeans radiation laws and used Occam's razor logic to formulate the quantum hypothesis, even resisting that hypothesis as it became more obvious that it was correct.
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At the time, however, the atomic theory was considered more complex because it implied the existence of invisible particles that had not been directly detected. Ernst Mach and the logical positivists rejected John Dalton 's atomic theory until the reality of atoms was more evident in Brownian motion , as shown by Albert Einstein. At the time, however, all known waves propagated through a physical medium, and it seemed simpler to postulate the existence of a medium than to theorize about wave propagation without a medium.
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Likewise, Newton's idea of light particles seemed simpler than Christiaan Huygens's idea of waves, so many favored it. In this case, as it turned out, neither the wave—nor the particle—explanation alone suffices, as light behaves like waves and like particles. Three axioms presupposed by the scientific method are realism the existence of objective reality , the existence of natural laws, and the constancy of natural law. Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified. Occam's razor and parsimony support, but do not prove, these axioms of science. The general principle of science is that theories or models of natural law must be consistent with repeatable experimental observations. This ultimate arbiter selection criterion rests upon the axioms mentioned above.
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For example, Newtonian, Hamiltonian and Lagrangian classical mechanics are equivalent. Physicists have no interest in using Occam's razor to say the other two are wrong. Likewise, there is no demand for simplicity principles to arbitrate between wave and matrix formulations of quantum mechanics. Science often does not demand arbitration or selection criteria between models that make the same testable predictions.
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George C. Williams in his book Adaptation and Natural Selection argues that the best way to explain altruism among animals is based on low-level i. Altruism is defined by some evolutionary biologists e. Alexander, ; W. Hamilton, as behavior that is beneficial to others or to the group at a cost to the individual, and many posit individual selection as the mechanism that explains altruism solely in terms of the behaviors of individual organisms acting in their own self-interest or in the interest of their genes, via kin selection.
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Williams was arguing against the perspective of others who propose selection at the level of the group as an evolutionary mechanism that selects for altruistic traits e. Wilson, The basis for Williams' contention is that of the two, individual selection is the more parsimonious theory. In doing so he is invoking a variant of Occam's razor known as Morgan's Canon : "In no case is an animal activity to be interpreted in terms of higher psychological processes, if it can be fairly interpreted in terms of processes which stand lower in the scale of psychological evolution and development.
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However, more recent biological analyses, such as Richard Dawkins ' The Selfish Gene , have contended that Morgan's Canon is not the simplest and most basic explanation. Dawkins argues the way evolution works is that the genes propagated in most copies end up determining the development of that particular species, i. Zoology provides an example. Muskoxen , when threatened by wolves , form a circle with the males on the outside and the females and young on the inside.
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This is an example of a behavior by the males that seems to be altruistic. The behavior is disadvantageous to them individually but beneficial to the group as a whole and was thus seen by some to support the group selection theory. Another interpretation is kin selection: if the males are protecting their offspring, they are protecting copies of their own alleles. Engaging in this behavior would be favored by individual selection if the cost to the male musk ox is less than half of the benefit received by his calf — which could easily be the case if wolves have an easier time killing calves than adult males. It could also be the case that male musk oxen would be individually less likely to be killed by wolves if they stood in a circle with their horns pointing out, regardless of whether they were protecting the females and offspring. That would be an example of regular natural selection — a phenomenon called "the selfish herd". Systematics is the branch of biology that attempts to establish patterns of relationship among biological taxa, today generally thought to reflect evolutionary history.
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It is also concerned with their classification. There are three primary camps in systematics: cladists, pheneticists, and evolutionary taxonomists. Cladists hold that classification should be based on synapomorphies shared, derived character states , pheneticists contend that overall similarity synapomorphies and complementary symplesiomorphies is the determining criterion, while evolutionary taxonomists say that both genealogy and similarity count in classification in a manner determined by the evolutionary taxonomist. Cladistic parsimony or maximum parsimony is a method of phylogenetic inference that yields phylogenetic trees more specifically, cladograms.
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Cladograms are branching, diagrams used to represent hypotheses of relative degree of relationship, based on synapomorphies. Cladistic parsimony is used to select as the preferred hypothesis of relationships the cladogram that requires the fewest implied character state transformations or smallest weight, if characters are differentially weighted. Critics of the cladistic approach often observe that for some types of data, parsimony could produce the wrong results, regardless of how much data is collected this is called statistical inconsistency, or long branch attraction. However, this criticism is also potentially true for any type of phylogenetic inference, unless the model used to estimate the tree reflects the way that evolution actually happened. Because this information is not empirically accessible, the criticism of statistical inconsistency against parsimony holds no force.
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Other methods for inferring evolutionary relationships use parsimony in a more general way. Likelihood methods for phylogeny use parsimony as they do for all likelihood tests, with hypotheses requiring fewer differing parameters i. Thus, complex hypotheses must predict data much better than do simple hypotheses before researchers reject the simple hypotheses.
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Recent advances employ information theory , a close cousin of likelihood, which uses Occam's razor in the same way. Of course, the choice of the "shortest tree" relative to a not-so-short tree under any optimality criterion smallest distance, fewest steps, or maximum likelihood is always based on parsimony [58] Francis Crick has commented on potential limitations of Occam's razor in biology. He advances the argument that because biological systems are the products of an ongoing natural selection, the mechanisms are not necessarily optimal in an obvious sense.
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He cautions: "While Ockham's razor is a useful tool in the physical sciences, it can be a very dangerous implement in biology. It is thus very rash to use simplicity and elegance as a guide in biological research. In biogeography , parsimony is used to infer ancient vicariant events or migrations of species or populations by observing the geographic distribution and relationships of existing organisms. Given the phylogenetic tree, ancestral population subdivisions are inferred to be those that require the minimum amount of change. Main article: Existence of God In the philosophy of religion , Occam's razor is sometimes applied to the existence of God.
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William of Ockham himself was a Christian. He believed in God, and in the authority of Scripture; he writes that "nothing ought to be posited without a reason given, unless it is self-evident literally, known through itself or known by experience or proved by the authority of Sacred Scripture. However, unlike many theologians of his time, Ockham did not believe God could be logically proven with arguments. To Ockham, science was a matter of discovery, but theology was a matter of revelation and faith. He states: "only faith gives us access to theological truths.
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The ways of God are not open to reason, for God has freely chosen to create a world and establish a way of salvation within it apart from any necessary laws that human logic or rationality can uncover. Thomas Aquinas , in the Summa Theologica , uses a formulation of Occam's razor to construct an objection to the idea that God exists, which he refutes directly with a counterargument: [62] Further, it is superfluous to suppose that what can be accounted for by a few principles has been produced by many. But it seems that everything we see in the world can be accounted for by other principles, supposing God did not exist. For all natural things can be reduced to one principle which is nature; and all voluntary things can be reduced to one principle which is human reason, or will.
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Therefore there is no need to suppose God's existence. In turn, Aquinas answers this with the quinque viae , and addresses the particular objection above with the following answer: Since nature works for a determinate end under the direction of a higher agent, whatever is done by nature must needs be traced back to God, as to its first cause.
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But you can say that as you approach 1, the limit is 2. Answers without supporting. Ap calculus unit 1 progress check frq part a answers Ap calculus unit 1 progress check frq part a answers. Unlike the multiple-choice section, which is scored by a computer, the free-response section is graded by high school and college teachers. Part b is. Here are the answers to this year's AP Chem free response questions. Feel free to leave any questions or comments here! The free response questions are each designed to be answered in about 12 minutes each, and the investigative task should take approximately 30 minutes.
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Cod mobile best perks reddit Legal self defense weapons california If a student needs the answers to the AP Chemistry Free Response questions because they have trouble knowing the answers it is best to ask the teacher for help. The answers are not online Course Overview. The student will be able to work the problems from a graphical, numerical, and analytical point of view and will then be able to communicate their solutions both verbally and in written form. Find and follow posts tagged ap biology on Tumblr. Taking Bio in 9th Grade: The mitochondria is the powerhouse of the cell. Taking AP Bio in 11th Grade: The mitochondria is the powerhouse of the cell because it takes glucose and oxygen and breaks them down through the process of glycolysis and produces a net of 2 ATP and 2 pyruvate which in turn goes through a transition reaction and the Kreb AP Chemistry Test Prep for educators ap statistics free response questions answers.
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Following the partition of Ireland and the independence of the Irish Free State in , which left Northern Ireland as the only part of the island of Ireland within the United Kingdom, the name was changed to the "United Kingdom of Great Britain and Northern Ireland". After conquering England , they seized large parts of Wales , conquered much of Ireland and were invited to settle in Scotland , bringing to each country feudalism on the Northern French model and Norman-French culture. Asserting its independence in the Declaration of Arbroath , Scotland maintained its independence thereafter, albeit in near-constant conflict with England. The English monarchs, through inheritance of substantial territories in France and claims to the French crown, were also heavily involved in conflicts in France, most notably the Hundred Years War , while the Kings of Scots were in an alliance with the French during this period.
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George's , Bermuda. Settled in , the town is the oldest continuously-inhabited English town in the New World. Although the monarchy was restored , the Interregnum along with the Glorious Revolution of and the subsequent Bill of Rights , and the Claim of Right Act ensured that, unlike much of the rest of Europe, royal absolutism would not prevail, and a professed Catholic could never accede to the throne. The British constitution would develop on the basis of constitutional monarchy and the parliamentary system. During this period, particularly in England, the development of naval power and the interest in voyages of discovery led to the acquisition and settlement of overseas colonies , particularly in North America and the Caribbean. On 1 May , the Kingdom of Great Britain was formed, the result of Acts of Union being passed by the parliaments of England and Scotland to ratify the Treaty of Union and so unite the two kingdoms.
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The Jacobites were finally defeated at the Battle of Culloden in , after which the Scottish Highlanders were brutally suppressed. British imperial ambition turned towards Asia, particularly to India. The world's oldest international human rights organisation, Anti-Slavery International , was formed in London in Alongside the formal control it exerted over its own colonies, British dominance of much of world trade meant that it effectively controlled the economies of many regions , such as Asia and Latin America. During the century, the population increased at a dramatic rate, accompanied by rapid urbanisation, causing significant social and economic stresses. Canada , Australia , and New Zealand became self-governing dominions. The Labour Party emerged from an alliance of trade unions and small socialist groups in , and suffragettes campaigned from before for women's right to vote. More than , British soldiers died on the battlefields of the First World War.
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After the war, Britain received the League of Nations mandate over a number of former German and Ottoman colonies. The British Empire reached its greatest extent, covering a fifth of the world's land surface and a quarter of its population. Northern Ireland remained part of the United Kingdom. A wave of strikes in the mids culminated in the General Strike of Britain had still not recovered from the effects of the war when the Great Depression — occurred.
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This led to considerable unemployment and hardship in the old industrial areas, as well as political and social unrest in the s, with rising membership in communist and socialist parties. A coalition government was formed in Winston Churchill became prime minister and head of a coalition government in Despite the defeat of its European allies in the first year of the war, Britain and its Empire continued the fight alone against Germany. Churchill engaged industry, scientists, and engineers to advise and support the government and the military in the prosecution of the war effort. Urban areas suffered heavy bombing during the Blitz. There were eventual hard-fought victories in the Battle of the Atlantic , the North Africa campaign and the Italian campaign.
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The graph would be a negative curve to the 90 degree Organize your answers as clearly and neatly as possible. You might want to label your answers according to the sub-part, such as a , b , c , etc. This will assist you in organizing your thoughts, as well as helping to ensure that you answer all the parts of the free-response question. E A plane mirror produces a virtual image that is the same size as the object in all cases. Free Response Answers 1. The index of refraction for the glass is very nearly equal to that for the immersion oil.
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