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  • 73 pages material+para+lab
    • material+para+lab
    • University of Uyo
    • tr
    • TRRTY tryy - Spring 2016
    • Laboratorio 1 Procedimientos Bsicos BIOSEGURIDAD EN EL LABORATORIO DE MICROBIOLOGA EN EL LABORATORIO USAR DELANTAL EN EL MESN SOLO MATERIALES DE TRABAJO SENTARNOS SOLO EN LAS SILLAS NO COMER, BEBER NI FUMAR, NI HABLAR POR CELULAR CABELLO RECOGIDO MAN
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    material+para+lab

  • 1 pages dufdj (47).docx
    • dufdj (47).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • particularly great because mathematicians generally regard these limit 66 3: Correction for Correlations theorems as the most important and sophisticated fruits of probability theory, and have a tendency to use language which implies that they are proving
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    dufdj (47).docx

  • 1 pages dufdj (61).docx
    • dufdj (61).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • is, the initial vector (3117) is then equal but for normalization to the eigenvector x1 in (3111), so the initial vector remains unchanged by the matrix (3105). In general, of course, there is no reason why this simplifying condition should hold. Yet in t
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    dufdj (61).docx

  • 1 pages dufdj (18).docx
    • dufdj (18).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • of coin tossing and see just how the method of tossing affects the results by direct physical influence. Chap. 3: ELEMENTARY SAMPLING THEORY 55 xi = 1 occurs, how many times xi = 2 occurs, etc. Such a distribution is called exchangeable; as we shall find
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    dufdj (18).docx

  • 1 pages dufdj (39).docx
    • dufdj (39).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • replace it in the urn before drawing the next ball. This case, of sampling with replacement, is enormously more complicated conceptually, but with some assumptions usually made, ends up being simpler mathematically, than sampling without replacement. For,
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    dufdj (39).docx

  • 1 pages dufdj (40).docx
    • dufdj (40).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • drew another ball, then it was left lying on the top of the other balls (or in the top layer of balls); and so it is more likely to be drawn again than any other specified ball, whose location in the urn is unknown. But this upsets the whole basis of our
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    dufdj (40).docx

  • 1 pages dufdj (68).docx
    • dufdj (68).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • 29)]. But even when one manages to avoid actual error, to restrict probability theory to problems of physical causation is to lose its most important applications. The extent of this restrictionand the magnitude of the missed opportunitydoes not seem to b
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    dufdj (68).docx

  • 1 pages dufdj (25).docx
    • dufdj (25).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • ways, with the same result. If the three results were not the same, we would have found an inconsistency in our rules, 58 3: Expectations of the kind we sought to prevent by Coxs functional equation arguments in Chapter 2. This is a good example of what c
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    dufdj (25).docx

  • 1 pages dufdj (9).docx
    • dufdj (9).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • same probability for red on the first and second draws. Let us see whether this continues. For the third draw we have R3 = (R1 + W1)(R2 + W2)R3 = R1R2R3 + R1W2R3 + W1R2R3 + W1W2R3 (336) and so P(R3|B) = M N M 1 N 1 M 2 N 2 + M N NMN1M1N2+NMNMN1M1N 2 + N
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    dufdj (9).docx

  • 1 pages dufdj (16).docx
    • dufdj (16).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • state of knowledge about the sounds Toscanini elicited from his orchestra many years ago. As this suggests, and as we shall verify later, a fully adequate theory of nonequilibrium phenomena such as sound propagation, also requires that backward logical in
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    dufdj (16).docx

  • 1 pages dufdj (60).docx
    • dufdj (60).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • But surveying them, we note that a remarkable simplification occurs if they satisfy p = q. (3131) For then we have p 1 = p, q 1 = q, + = q (3132) and our main results (3118), (3 128) collapse to P(Rk|C) = p, all k (3133) P(Rk|RjC) = P(Rj |RkC) = p + q q |
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    dufdj (60).docx

  • 1 pages dufdj (28).docx
    • dufdj (28).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • same meaning but sometimes one is easier to read than the other. Like most of the standard terms that arose out of the distant past, the term expectation seems singularly inappropriate to us; for it is almost never a value that anyone expects to find. Ind
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    dufdj (28).docx

  • 1 pages dufdj (20).docx
    • dufdj (20).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • P(R1R2|B) = M(M 1) N(N 1) (345) and likewise P(WjRk|B) = P(W1R2|B) = (N M)M N(N 1) . (3 46) Therefore by the product rule P(Rk|RjB) = P(RjRk|B) P(Rj |B) = M 1 N 1 (347) and P(Rk| WjB) = P(WjRk|B) P(Wj |B) = M N 1 (348) for all j < k. By (340), the results
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    dufdj (20).docx

  • 1 pages dufdj (58).docx
    • dufdj (58).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • general product rule holds, as always: P(RkRj |C) = P(Rk|RjC) P(Rj |C) = P(Rj |RkC) P(Rk|C). (3129) Therefore, since we have seen that P(Rk|C) 6= P(Rj | C), it follows that P(Rj |RkC) 6= P(Rk|RjC). (3130) The backward inference is still possible, but it i
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    dufdj (58).docx

  • 1 pages dufdj (6).docx
    • dufdj (6).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • Distribution, N, M, n = 99, 50, 10. example Press, W. H., et al, (1986) list two routines that will calculate the generalized complex hypergeometric distribution for any values of a, b and c. Tables 3.1 and 3.2 give the hypergeometric distribution for N =
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    dufdj (6).docx

  • 1 pages dufdj (38).docx
    • dufdj (38).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • no match at all. Exercise 3.5. N balls are tossed into M urns; there are evidently MN ways this can be done. If the robot considers them all equally likely, what is its probability that each urn receives at least one ball? Sampling With Replacement Up to
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    dufdj (38).docx

  • 1 pages dufdj (33).docx
    • dufdj (33).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • N 2 N M N r 1 N (382) and in the limit N , M , M/N f we have 1 Nr M r f r r! . (383) Likewise 1 Nnr M 1 n r (1 f) nr (n r)! (384) 1 Nn N n 1 n! . (385) In principle we should, of course, take the limit of the product in (381), not the product of the lim
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    dufdj (33).docx

  • 1 pages dufdj (63).docx
    • dufdj (63).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • from a population. In a few cases, such as recording counts from a radioactive source, survey sampling, and industrial quality control testing, one is quite literally drawing from a real, finite population, and the urn analogy is particular apt. Then the
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    dufdj (63).docx

  • 1 pages dufdj (15).docx
    • dufdj (15).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • evidence for a causal influence: is a new medicine more effective, or a new engineering design more reliable? Does a new anti-crime law reduce the incidence of crime? Our study of hypothesis testing starts in Chapter 4. In all the sciences, logical infere
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    dufdj (15).docx

  • 1 pages dufdj (26).docx
    • dufdj (26).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • more than one, but it reduces the number of balls in the urn available for the first draw by 2 (because it assures the robot that there are two later draws in which two balls are removed). So let us try tentatively to interpret the result (357) as P(R1| R
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    dufdj (26).docx

  • 1 pages dufdj (46).docx
    • dufdj (46).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • making a practical compromise and being, of necessity, content with an approximate solution. That is something we have to do in all areas of applied mathematics, and there is no reason to expect probability theory to be any different. Our objection is to
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    dufdj (46).docx

  • 1 pages dufdj (10).docx
    • dufdj (10).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • the context of the problem), their probabilities are often calculable. If they are not well chosen (as in the example of the penguins at the end of Chapter 2), then of course this procedure cannot help us. Chap. 3: ELEMENTARY SAMPLING THEORY 53 Logic Vers
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    dufdj (10).docx

  • 1 pages dufdj (59).docx
    • dufdj (59).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • extrapolating the forward solution backward in time, with quite bizarre and unphysical results. Therefore the reader is, in effect, conducting new research in doing the following exercise. Exercise 3.6. Find the explicit formula P(Rj |RkC) for the backwar
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    dufdj (59).docx

  • 1 pages dufdj (31).docx
    • dufdj (31).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • either color is declared to have color a. Then from (375) we must have on the one hand, h(ra, r3 rk|Na, N3 Nk) = Na ra N3 r3 Nk rk P P Ni ri (376) with Na = N1 + N2, ra = r1 + r2. (377) But the event ra can occur for any values of r1, r2 satisfying (377)
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    dufdj (31).docx

  • 1 pages dufdj (7).docx
    • dufdj (7).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • symmetry of the distribution about its peak: h(r| 100, 50, 10) = h(10 r|100, 50, 10). However, this is not so in general; changing N to 99 results in a slightly unsymmetrical peak as we see from Table 3.3. The symmetric peak in Table 3.1 arises as follows
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    dufdj (7).docx

  • 1 pages dufdj (67).docx
    • dufdj (67).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • independently of what we know about any other draw. Such prior information would take precedence over any amount of data. If we did not know the contents (M, N) of the urnsbut we knew they all had identical contentsthis strict independence would be lost,
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    dufdj (67).docx

  • 1 pages dufdj (13).docx
    • dufdj (13).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • he would say that the probability for a particular face in tossing a die is not a physical property of the die [as Cramer (1946) insisted] but rather is an objective property of the whole experimental arrangement, the die plus the method of tossing. Of co
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    dufdj (13).docx

  • 1 pages dufdj (2).docx
    • dufdj (2).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • complicated, it has some surprisingly simple properties. The most probable value of r is found to within one unit by setting h(r 0 ) = h(r 0 1) and solving for r 0 . We find r 0 = (n + 1)(M + 1) N + 2 . (326) If r 0 is an integer, then r 0 and r 0 1 are j
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    dufdj (2).docx

  • 1 pages dufdj (5).docx
    • dufdj (5).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • and the quartiles. Then the (median) (interquartile distance) will provide a good enough idea of the robots prediction and its probable accuracy. That is, on the information given to the robot, the true value of r is about as likely to lie in this interva
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    dufdj (5).docx

  • 1 pages dufdj (32).docx
    • dufdj (32).docx
    • University of Uyo
    • Micro Economics
    • ECON 211 - Summer 2016
    • complicated mathematically, the hypergeometric distribution arises from a problem that is very clear and simple conceptually; there are only a finite number of possibilities and all the above results are exact for the problems as stated. As an introductio
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    dufdj (32).docx

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