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Course: HST 101, Spring 2009
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Alexander 1. Hamiltons economic program was designed prima r ily to (A) prepare the United States for war in the event Bri tain failed to vacate its posts in the Northwest (B) provide a platform for the f ledgling Federalist Partys 1792 campaign (C) establish the financial stability and credit of the new government (D) ensure northern dominance over the southern states in order to abolish slavery (E) win broad...

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Alexander 1. Hamiltons economic program was designed prima r ily to (A) prepare the United States for war in the event Bri tain failed to vacate its posts in the Northwest (B) provide a platform for the f ledgling Federalist Partys 1792 campaign (C) establish the financial stability and credit of the new government (D) ensure northern dominance over the southern states in order to abolish slavery (E) win broad political support for his own candidacy for the presidency in 1792 2. The development of the early nineteenth-centu ry concept of separate spheres for the sexes encouraged all of the following EXCEPT (A) acceptance of a woman as the intellectual equal of a man (B) idealization of the lady (C) designation of the home as the appropriate place for a woman (D) emphasis on child care as a prime duty of a woman (E) establishment of a moral climate in the home 3. The presidential election of 1840 is often considered the fi rst modern election because (A) the slavery issue was first raised in this campaign (B) there was a very low tu rnout of eligible voters (C) voting patterns were similar to those later established in the 1890s (D) both parties for the first time widely campaigned among all the eligible voters (E) a second era of good feeling had just come to a close, marking a new departure in politics 4. The graph above refutes which of the following statements? (A) There were more Black people than White people in the antebellum South. (B) Most southern families held slaves. (C) Most southern families lived in rural areas. (D) The southern population was much smaller than that of the North. (E) Slaveholders were an extremely powerful group. 5. F rederick Jackson Tu r ne rs frontier hypothesis focused on the importance of (A) the t raditions of western European culture (B) the absence of a feudal aristocracy (C) Black people and Black slavery (D) the conflict between capitalists and workers (E) the existence of cheap unsettled land 6. Du r ing the closing decades of the nineteenth centu ry, farmers complained a bout all of the following EXCEP T (A) r ising commodity prices (B) high interest charges (C) high freight rates (D) high storage costs (E) large middleman profits 7. The Roosevelt Corolla ry to the Monroe Doctr ine did which of the following? (A) Prohibited United States intervention in the Caribbean. ( B) Warned against European seizure of the Panama Canal. (C) Sought to end the wave of nationalization of American-owned property in the Caribbean. (D) Declared the United States to be the policeman of the Western Hemisphere. (E) Provided United States mili tary support for democratic revolutions in Latin America. 8. One of the p rincipal reasons the noble experiment of P rohibition failed was t hat it led to an enormous increase in (A) drinking among minors (B) absenteeism among factory workers (C) the divorce rate (D) child abuse (E) law enforcement costs 9. B rown v. Board of Education of Topeka w as a Supreme Court decision that (A) was a forerunner of the Kansas-Nebraska Act (B) established free public colleges in the United States (C) declared racially segregated public schools inherently unequal (D) established free public elementary and secondary schools in the United States (E) provided for federal support of parochial schools 10. Joseph McCa rthys investigative tactics found support among many A mericans because (A) evidence substantiated his charges against the army (B) there was widespread fear of communist infilt ration of the United States (C) both Truman and Eisenhower supported him (D) he worked closely with the FBI (E) he correctly identified numerous communists working in the State Department 11. The Tet offensive of 1968 dur ing the Vietnam War demonstrated that (A) bombing North Vietnam had severely curtailed Vietcong supplies (B) the army of South Vietnam was in control of the South (C) American strategy was working (D) a negotiated settlement was in the near future ( E) the Vietcong could attack major cities throughout South Vietnam 12. Liberty of conscience was defended by Roger Williams on the grounds that (A) all religions were equal in the eyes of God (B) the signers of the Mayflower Compact had guaranteed i t (C) Puritan ideas about sin and salvation were outmoded (D) theological t ruths would emerge from the clash of ideas (E) the state was an improper and ineffectual agency in matters of the spirit 13. By the end of the seventeenth centu ry, which of the following was t rue of w omen in New England? (A) They had begun to challenge their subordinate role in society. (B) They were a majority in many church congregations. (C) They voted in local elections. (D) They frequently divorced their husbands. (E) They could lead town meetings. 14. The Fi rst Great Awakening led to all of the following EXCEPT (A) separatism and secession from established churches (B) the renewed persecution of witches (C) the growth of institutions of higher learning (D) a f lourishing of the missionary spirit (E) a greater appreciation for the emotional experiences of faith 15. The Embargo Act of 1807 had which of the following effects on the United S tates? (A) I t severely damaged American manufacturing. (B) I t enriched many cotton plantation owners. (C) I t disrupted American shipping. (D) I t was ruinous to subsistence farmers. (E) I t had li t t le economic impact. 16. The National Road was constructed p rima r ily for the purpose of (A) demarcating the southwestern boundary of the Louisiana Purchase ( B) promoting t rade and communication with the Old Northwest (C) opening the Southwest to ranchers (D) assisting the movement of settlers to the Oregon Country (E) relieving overpopulation and crowding in the Northeast 17. The idea of M anifest Destiny included all of the following beliefs EXCEPT: (A) Commerce and industry would decline as the nation expanded i ts agricultural base. (B) The use of land for settled agriculture was preferable to its use for nomadic hunting. (C) Westward expansion was both inevitable and beneficial. (D) God had selected America as a chosen land and people. (E) The ultimate extent of the American domain was to be from the t ropics to the Arctic. 18. Which of the following statements about woman suffrage is t r ue? (A) The six states of New England were the first to have complete woman suffrage. (B) Woman suffrage was int roduced into the South during Radical Reconstruction. (C) No state granted woman suffrage before 1900. (D) The only states with complete woman suffrage before 1900 were west of the Mississippi. (E) California and Oregon were the first states to have complete woman suffrage. 19. The American Federation of Labor under the leadership of Samuel Gompers o rganized (A) skilled workers in craft unions in order to achieve economic gains (B) all industrial and agricultural workers in one big union (C) unskilled workers along industrial lines (D) workers and intellectuals into a labor party for political action (E) workers into a fraternal organization to provide unemployment and old-age benefits 20. I n the period 18901915, all of the following were generally t rue about African A mericans EXCEPT: (A) Voting r ights previously gained were denied through changes in state laws and constitutions. (B) Back-to-Africa movements were widely popular among African Americans in urban a reas. (C) African American leaders disagreed on the principal strategy for attaining equal r ights. ( D) Numerous African Americans were lynched, and mob attacks on African American i ndividuals occurred in both the North and the South. (E) African Americans from the ru ral South migrated to both southern and northern cities. 21. Conservative Republican opponents of the T reaty of Versailles argued that the L eague of Nations would (A) isolate the United States from world postwar affairs (B) prevent the United States from seeking reparations from Germany (C) violate President Wilsons own Fourteen Points (D) limit United States sovereignty (E) give England and France a greater role than the United States in maintaining world peace 22. Which of the following best characterizes the stance of the w r iters associated w ith the litera ry flowering of the 1920s, such as Sinclai r Lewis and F. Scott F itzgerald? (A) Sympathy for Protestant fundamentalism (B) Nostalgia for the good old days (C) Commitment to the cause of racial equality (D) Advocacy of cultural isolationism (E) Criticism of middle-class conformity and materialism 23. Which of the following is t r ue of the forced relocation of Japanese Americans f rom the West Coast du ring the Second World War? (A) President Roosevelt claimed that mili tary necessity justified the action. (B) The Supreme Court immediately declared the action unconstitutional. (C) The relocation was implemented according to congressional pro-visions for the i nternment of dissidents. (D) The Japanese Americans received the same t reatment as that accorded German A mericans and I talian Americans. (E) Few of those relocated were actually United States citizens. 24. Which of the following was an immediate consequence of the Bay of Pigs i ncident? ( A) Congress demanded United States withdrawal from the Panama Canal Zone. (B) The Soviet Union sent missiles to Cuba. (C) Americans began to view nuclear power plants as dangerous. (D) The United States ended its military occupation of Japan. (E) China entered the Korean War. 25. The high inflation rates of the late 1960s and early 1970s were pr ima rily the r esult of (A) major state and federal tax increases (B) increased investment in major industries (C) spending on social-welfare programs and the Vietnam War (D) a decline in foreign t rade (E) deregulation of key t ransportation and defense industries 26. Which of the following was t rue of a mar r ied woman in the colonial era? (A) She would be sentenced to debtors prison for debts incurred by her husband. (B) She could vote as her husbands proxy in elections. (C) She generally lost control of her property when she mar ried. (D) She was the beneficiary by law of her husbands estate. (E) Her legal r ights over her children were the same as those of her husband. 27. Which of the following colonies requi red each community of 50 or more f amilies to provide a teacher of reading and w r i ting? (A) Pennsylvania (B) Massachusetts (C) Virginia (D) Maryland (E) Rhode Island 28. The area marked X on the map was par t of (A) Massachusetts Western Reserve (B) the Northwest Terri tory (C) the Louisiana Purchase (D) the Mexican Cession (E) the Oregon Count ry 29. I n the early years of the textile industry in Lowell, Massachusetts, owners of t he textile mills were best known for thei r (A) humanitarian refusal to hire women and children as factory operatives (B) brutal t reatment of their workforces (C) idealistic efforts to avoid the worst evils of English industrialization (D) profit-motivated efforts to replicate the factory system of the English Industrial Revolution (E) pioneering efforts to establish labor unions 30. At the beginning of the Civil War, Southerners expressed all of the following e xpectations EXCEPT: (A) The materialism of the North would prevent Northerners from fighting an idealistic war. (B) Great Bri tain would intervene on the side of the South in order to preserve i ts source of cotton. (C) Northern unity in the struggle against the Southern states would eventually break. ( D) The economic and mili tary resources of the South would outlast those of the North. (E) The justice of the Souths cause would prevail. 31. Which of the following constitutes a significant change in the t reatment of A merican I ndians du r ing the last half of the nineteenth centu ry? (A) The beginnings of negotiations with individual t r ibes (B) The start of a removal policy (C) The abandonment of the reservation system (D) The admission of all American Indians to the full r ights of United States citizenship (E) The division of the t r ibal lands among individual members 32. This, then, is held to be the duty of the man of wealth: to consider a l l surplus revenues which come to him simply as t rust funds, which he is called upon to a dminister and strictly bound as a matter of duty to administer in the manner w hich, in his judgment, is best calculated to produce the most beneficial results for t he communitythe man of wealth thus becoming the mere agent and t rustee for h is poorer b rethren. T hese sentiments are most characteristic of (A) t ranscendentalism (B) pragmatism (C) the Gospel of Wealth (D) the Social Gospel (E) Reform Darwinism 33. M any Mexicans migrated to the United States du ring the F i rst World War because (A) revolution in Mexico had caused social upheaval and dislocation (B) immigration quotas for Europeans went unfilled as a result of the war (C) the war in Europe had disrupted the Mexican economy (D) American Progressives generally held liberal views on the issue of racial assimilation (E) the United States government offered Mexicans land in exchange for mili tary service 34. Which of the following has been viewed by some historians as an indication of strong anti-Catholic sentiment in the presidential election of 1928? (A) The increased political activity of the Ku K lux K lan ( B) The failure of the farm bloc to go to the polls (C) Alfred E. Smiths choice of Arkansas senator Joseph T. Robinson as his running mate (D) Alfred E. Smiths failure to carry a solidly Democratic South (E) Herbert Hoovers use of rugged individualism as his campaign slogan 35. Du r ing his presidency, Ha r r y S T r uman did all of the following EXCEPT (A) abolish the Tennessee Valley Authority (B) establish a new loyalty program for federal employees (C) extend Social Security benefits (D) order the desegregation of the armed forces (E) veto the Taft-Har tley Act 36. Which of the following best describes the Ha rlem Renaissance? (A) The rehabili tation of a decaying urban area (B) An outpouring of Black artistic and li terary creativity (C) The beginning of the NAACP (D) The most famous art show of the early twentieth century (E) The establishment of the back-to-Africa movement 37. Conscription policies in the Fi rst and Second World Wars differed significantly in that in the Second World War (A) African Americans were drafted into integrated units (B) conscientious objectors were not officially recognized (C) the draft began before the United States entered the conflict (D) the draft was administered at the regional and federal levels by the armed forces (E) exemptions were offered for a range of war-related occupations 38. All of the following concerns were addressed du ring the Hundred Days of t he New Deal EXCEPT (A) banking regulation (B) unemployment relief (C) agricultural adjustment (D) homeowner mortgage support ( E) court restructuring 39. Jimmy Ca rter and Ronald Reagan were simila r as presidential candidates in t hat both (A) articulated the publics desire for less involvement in foreign affairs (B) capitalized on their status as Washington outsiders (C) promised Congress increased control over domestic matters (D) renounced private fund-raising in support of their campaigns (E) had built national reputations as legislators 40. Richard N ixons 1968 political comeback to w in the presidency can be partly a tt r ibuted to (A) dissension within the Democratic Party over Vietnam (B) the defection of Black voters to the Republican Party (C) Nixons cordial relations with the news media (D) Nixons great popularity as Eisenhowers vice president (E) Nixons promise of immediate withdrawal of American forces from Vietnam
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Martin Luther - HST - 101
10.)Worcesterv.Georgia(1832) SamuelWorcester,amissionaryminister,refusedtoregisterorpledgehisallegianceto Georgialawbeforeenteringontothereservation,wheregoldhadbeendiscovered.Chief JusticeJohnMarshallheldthatstatelawsinterferingwithrelationsestablishedbe
Martin Luther - HST - 101
In the spring of 1851, Elijah, his wife, Lucia, and their four children, Richard, George, John, and Helen, left their home in Findlay, Ohio, and headed west for the Oregon Territory. They rode with 14 other wagons filled with emigrants wanting to start a
Martin Luther - HST - 101
Chapter 6 Basal Metabolic Rate(BMR)Bond Enthalpy(Bond Energy)Caloric ValueCalorimeterCarbohydrateChange of stateChemical fuelLaw of conservation of energyEndothermicEnergy densityEnthalpy changeEnthalpy of fusionEnthalpy of vaporizationExothermicFirst law
Martin Luther - HST - 101
425-443; 446-469 American L iteratu re (1820 1865) T H E L I T ERARY H E R I TAGE OF T H E YOUNG REPUBL IC Educated Americans familiar with Greek & Roman history & Euro history & l i terature Edward Taylors poems o Unpublished Benjamin Franklins autobiogr
Martin Luther - HST - 101
JacobIrbySlavery played a key role in American economy, politics, and social life prior to 1860. Slavery was the most controversial issue in pre-Civil War era in America. At the beginning of the nineteenth century, many new developments made slave labor
Martin Luther - HST - 101
1.The Spanish monopoly on trade and colonization of the New World ended with(A) (B) (C) (D) (E)Youleftthisquestionblank.YoushouldhaveselectedE.EXPLANATIONThedefeatoftheSpanishArmadaendedSpainsmonopolyontradeandcolonizationintheNewWorld.Afterwards,Gre
Martin Luther - HST - 101
Chapter 13 C. The Debate on Internal Improvements1. Jackson Vetoes the Maysville Road Bill (1830)TheVetoMessageproceedstoinsistthattheMaysvilleandLexingtonRoadisnota nationalbutalocalroadofsixtymilesinonlyonestate.Italsoassertsthepowercannotbe exercised
Martin Luther - HST - 101
1. The aging of the American population at the end of the 20th century was primarily due toA. fertility and mortality rates below their long-term averages.B. a record number of births after World War II.C. new methods of contraception and abortion.D.
Martin Luther - HST - 101
SolonRobinsonhadastrongviewpointontheissueofslavery;hebelievedthatthe greatestpunishmentthataSouthernslavecouldsufferfromwasthefreedomandlibertywhich Godhaddeprivedhimorherfrom.Heclaimsthatsincethereismorewelltreatedslavesit makesupforallthemaltreatedslav
Martin Luther - HST - 101
As the United States emerged from its colonial status and sought independence from Britain, its own policies and action brought into being nonviolent protest actions that were early forerunners of the modern-day Civil Rights Movement. However, the immigra
Martin Luther - HST - 101
The New Nation Terms:1. Articles of Confederation 2. Critical Period 3. Land Ordinance of 1785 4. Northwest Ordinance of 1787 5. Shays Rebellion 6. Virginia Plan (large state plan) 7. New Jersey Plan (small state plan) 8. Connecticut (Great) Compromise 9
Martin Luther - HST - 101
Wanted1.)http:/robertarood.files.wordpress.com/2008/07/poe1.jpg 2.) 3.) 4.) Edgar Allan Poe Born in Boston, Massachusetts, on January 19, 1809 (Merriman) Editor of the Southern Literary Messenger in Richmond (Merriman) 58 186 pounds Black eyes and hair
Duke - MATH - 241
Mathematics 241, Problem Set #1, due August 31, 2009Write clear proofs that have good grammar and consist of complete sentences. 1. Prove that a function from a Metric Space < X, > to a metric space < Y, > is continuous at x X if and only if, given and >
Duke - MATH - 241
Mathematics 241, Problem Set #2, due September 7, 2009Write clear proofs that have good grammar and consist of complete sentences.Royden, page 55, #4.Royden, page 58, #6,7,8.Royden, page 64, #10,13.Note. Number 13 is long but rewarding. The previous
Duke - MATH - 241
HOMEWORK 2 SOLUTIONSProblem 1 Fix i1 , i2 , ., ik I. We shall show that Yi1 , .Yik are independent by showing thatkPcfw_Yi1 ti , ., Yik tk =l=1P(Yil tl ),t1 , t2 , .tk R.Step1: For any bounded continuous functions f1 , f2 , ., fk , we havek kEl
Duke - MATH - 241
Mathematics 241, Problem Set #3, due September 14, 2009Write clear proofs that have good grammar and consist of complete sentences.Royden, page 70, #19,21,23,24.Royden, page 73, #29,30.
Duke - MATH - 241
Mathematics 241, Problem Set #4, due September 21, 2009Write clear proofs that have good grammar and consist of complete sentences. 1. Royden, page 89, #32. Royden, page 89, #43. Royden, page 89, #54. Royden, page 89, #65. Royden, page 89, #76. Royd
Duke - MATH - 241
Mathematics 241, Problem Set #5, due September 28, 2009 (dont turn in)Write clear proofs that have good grammar and consist of complete sentences. Royden, page 96, #20,21,24 Royden, page 94, #16, 17
Duke - MATH - 241
Mathematics 241, Problem Set #6, due October 7, 2009Write clear proofs that have good grammar and consist of complete sentences. Royden, page 40, #22 Royden, page 46, #37 Royden, page 50, #48 Royden, page 64, #14Hint: follow the Beale notes given out in
Duke - MATH - 241
Mathematics 241, Problem Set #7, due October 12, 2009Write clear proofs that have good grammar and consist of complete sentences. Royden, page 101, #1,4.Royden, page 104, # 7, 10.Royden, page 110, #12, 14, 15
Duke - MATH - 241
Mathematics 241, Problem Set #8, due October 21, 2009Write clear proofs that have good grammar and consist of complete sentences. Royden, page 122, #7Royden, page 126, # 9, 12, 14, 15, 16, 17Royden, page 135, #22
Duke - MATH - 241
Mathematics 241, Problem Set #9, due October 28, 2009Write clear proofs that have good grammar and consist of complete sentences. Royden, page 258, #5a,b,cRoyden, page 267, # 19, 21, 22Royden, page 275, #27, 28Royden, page 279, #33, 35
Duke - MATH - 241
Mathematics 241, Problem Set #10, due November 4, 2009Write clear proofs that have good grammar and consist of complete sentences.Royden, page 291, #1.Royden, page 298, #3, 4.Royden, page 310, #21,24,25,29.8. (a) Let f (x) = x1 sin x for x > 0 and f
Duke - MATH - 241
831 Theory of Probability Fall 2009 Homework 2Due Tuesday, September 221. Let cfw_Xn,i : n N, i I be real-valued random variables on (, F, P ). Assume that for each n N, the variables cfw_Xn,i : i I are independent. Assume that for each i I there is a r
Duke - MATH - 241
831 Theory of Probability Fall 2009 Homework 3Due Thursday, October 11. Let > 0. Show that, for a > 0, lim en (n)k k! k : 0kna = 0, if a < 1, if a > .nHint: apply the WLLN to Poisson random variables. 2. For each n N let cfw_Xn,k : 1 k n be IID random
Duke - MATH - 241
831 Theory of Probability Fall 2009 Homework 4Due Tuesday, October 131. Monte Carlo integration. Assume given a continuous function u on [0, 1] such that 0 u(x) 1. We use u to create an array of cfw_0, 1-valued random variables as follows: let cfw_Xn,k
Duke - MATH - 241
831 Theory of Probability Fall 2009 Homework 5Due Tuesday, October 271. Let cfw_Xn , X be real random variables. d (a) Suppose Xn X in probability. Show that then also Xn X . (b) Suppose Xn converges in distribution to a constant c. Show that then Xn c
Duke - MATH - 241
831 Theory of Probability Fall 2009 Homework 6Due Thursday, November 121. IID variables close up. Let cfw_Yk be i.i.d. random variables on R with a common continuous density f . As we put more and more points Yk down they tend to concentrate so let us
Duke - MATH - 241
HOMEWORK 3 SOLUTIONSProblem 1 A basic property of Poisson random variables is that if cfw_Xk are i.i.d. Poisson(), then Sn is Poisson(n). Thus, e-n (n)k = P(Sn na) = P(Sn - n n(a - ). k! >0 P Hence, if a < we have P(Sn - n n(a - ) P(|Sn - n| n( - a) 0,
Duke - MATH - 241
HOMEWORK 4 SOLUTIONSProblem 1 First observe that (1) n1 ESn = n11knEXn,k =1knn 1 uk nwhich in particular is the Riemann sum of u for the partition1k : 1 k n . Since u is n integrable, we know that that the Riemann sum converges to the integral of
Duke - MATH - 241
HOMEWORK 5 SOLUTIONS Problem 1 a) We can show this immediately using Corollary 6.4 from Chapter 1 of Durret. b)Let X = c and for any > 0 dene the open interval A = (c , c + ). The boundary A = cfw_c , c + , therefore Pcfw_X A = 0. By the Portmanteau Theo
Duke - MATH - 241
205B homework, week 2; due Thursday February 5 Durrett Chapter 5 Exercises 1.6, 1.7, 1.8, 2.3, 2.5, 2.10, 2.111
Duke - MATH - 241
205B homework, week 3; due Thursday February 12 Durrett Chapter 5 Exercises 4.3, 4.4, 4.8, 4.10 1. Give an example to show that, if Xn is a Markov chain, then f (Xn ) need not be a Markov chain. 2. Let A and B be disjoint subsets of a nite state space S .
Duke - MATH - 241
205B homework, week 4; due Thursday February 19Durrett Chapter 5 Exercises 5.7, 5.8, 5.11 1. Let (Xn ) be an irreducible Markov chain on S with transition matrix (p(x, y ). Let B be a nite subset of S such that the chain a.s. visits B innitely often. Let
Duke - MATH - 241
205B homework, week 5; due Thursday February 26 These are miscellaneous questions on Markov chains, not necessarily closely connected to this weeks class material.1. Let Xn be the Markov chain on states 0, 1, . . . , K with transition matrix p(i, i + 1)
Duke - MATH - 241
3. Let P (i, j ) be a Markov transition matrix on cfw_0, 1, 2, . . .. Give a simple necessary and sucient condition, in terms of P , for the following assertion to be true. For any pair i0 < j0 it is possible to construct (Xn , Yn ; n 0) such that 1. X is
Duke - MATH - 241
205B homework, week 6; due Thursday March 51. Let (Xn ) be an irreducible Markov chain on states I = cfw_0, 1, 2, . . .. Let g : I R be such that (a) Ei g (X1 ) g (i) for all i, with strict inequality for some i. (b) supi Ei |g (X1 ) g (i)| < . Prove tha
Duke - MATH - 241
4. Let (Xn , n 0) be a nite-state irreducible Markov chain with transition matrix P. Let f be a non-constant real-valued function and 0 < < 1 be such that j pij f (j ) = f (i) i. (i) Show that n f (Xn ) is a martingale. (ii) Let b be the rst hitting time
Duke - MATH - 241
205B homework, week 7; due Thursday March 12 Durrett section 4.3 Exercises 1, 2, 3, 4, 9, 10, 118
Duke - MATH - 241
205B homework, week 8; due Thursday March 19 1. Prove the following slight extension of Azumas inequality. Let (Mn ) be a martingales such that |Mn Mn1 | Kn for constants Kn . Then for x > 0n 1 P (|Mn M0 | x) 2 exp 2 x2 / i=1Ki2 .2. Suppose you have n
Duke - MATH - 241
205B Homework, Week 9; due Thursday Apr 2 Durrett Chapter 6 problems 1.7, 3.1, 3.4, 3.5.10
Duke - MATH - 241
205B Homework, Week 10; due Thursday Apr 9 Durrett Chapter 6 problems 7.1, 7.2, 7.4. 1. (This is a more careful statement of Durrett Chapter 6 Exercise 6.2.) Let (X1 , X2 , . . . ; Y1 , Y2 , . . .) be i.i.d. taking values 0 or 1 with probability 1/2 each.
Duke - MATH - 241
205B Homework, Week 11-12; due Thursday Apr 23 Durrett Chapter 7 problems 1.3, 2.4, 3.3, 3.6, 3.7, 5.312
Duke - MATH - 241
205B Homework, Week 13-14; due Thursday May 7 Durrett Chapter 7 problems 5.4, 6.1, 6.3, 7.113
Duke - MATH - 241
Lecture 1 : IntroductionWe will start with a simple combinatorial problem. Consider cfw_1, 11000 . How many elements x cfw_1, 11000 satisfy1000xi 50?i=1More generally, for any n N and > 0 how many elements x cfw_1, 1n satisfynxi n?i=1The answer i
Duke - MATH - 241
Lecture 2 : Ideas from measure theory2.1Probability spacesThis lecture introduces some ideas from measure theory which are the foundation of the modern theory of probability. The notion of a probability space is dened, and Dynkins form of the monotone
Duke - MATH - 241
Lecture 3 : Random variables and their distributions3.1Random variablesLet (, F ) and (S, S ) be two measurable spaces. A map X : S is measurable or a random variable (denoted r.v.) if X 1 (A) cfw_ : X ( ) A F for all A S One can write cfw_X A or (X A)
Duke - MATH - 241
Lecture 4: Expected Value4-1Lecture 4 : Expected ValueReferences: Durrett [Section 1.3]4.5Expected ValueDenote by (, F , P) a probability space. Denition 4.5.1 Let X : R be a F\B -measurable random variable. The expected value of X is dened by E(X )
Duke - MATH - 241
Lecture 5: Inequalities5-1Lecture 5 : Inequalities5.7InequalitiesLet X, Y etc. be real r.v.s dened on (, F , P). Theorem 5.7.1 (Jensens Inequality) Let be convex, E(|X |) < , E(|(X )|) < . Then (E(X ) E(X ) (5.11) Proof Sketch: As is convex, is the s
Duke - MATH - 241
Lecture 6 : DistributionsTheorem 6.0.1 (Hlders Inequality) If p, q [1, ] with 1/p + 1/q = 1 then o E(|XY |) |X |p |Y |q (6.1)Here |X |r = (E(|X |r )1/r for x [1, ); and |X | = inf cfw_M : P(|X | > M ) = 0. Proof: See the proof of (5.2) in the Appendix o
Duke - MATH - 241
Lecture 7 : Product Spaces7.3Product spaces and Fubinis TheoremiDenition 7.3.1 If (i , Fi ) are measurable spaces, i I (index set), form For simplicity, i = 1 .ii .i (write for this) is the space of all maps: I 1 . For i i , = (i : i I, i i ). is e
Duke - MATH - 241
Lecture 8: Weak Law of Large Numbers8-1Lecture 8 : Weak Law of Large NumbersReferences: Durrett [Sections 1.4, 1.5] The Weak Law of Large Numbers is a statement about sums of independent random variables. Before we state the WLLN, it is necessary to de
Salisbury - THET - 110
Review Pre-colonial o o Oral tradition Not even really necessarily theaterColonial Theater o o o Build traditional theaters for audiences can watch Bringing over European plays to be done Adapting European playsPost-Colonial Theater o o Often Political
McGill - CHEM - CHEM 204
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Shandong University - RTY - 11
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Shandong University - RTY - 11
HYDRAULIC E XCAVATORKomatsu PC128UU Used exavator gebrauchte baumaschinen gebrauchte kettenbagger PC 75UUPC128UUHydraulics The PC128uu features the same HydrauMind hydraulic system found on all other Avance Dash 6 excavators for greater control and smo
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NEXT GENERATION OF OPERATING SYSTEMS DESIGN BASED ON KNOWLEDGE ABSTRACTIONFURB University of Blumenau Campus IV R.Braz Wanka, 238 - CP 1507 CEP 89035-160 mattos@furb.brMauro Marcelo Mattos,Dr.ABSTRACT This work presents an overview of an endogenous sel
Shandong University - RTY - 11
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Shandong University - RTY - 11
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Shandong University - RTY - 11
PC128UU-2NET HORSEPOWER 64 kW 86 HP OPERATING WEIGHT 13,400 - 13,770 kg 29,450 - 30,360 lbHydraulics The PC128UU features the same HydrauMind hydraulic system found on all other Avance Dash 6 excavators for greater control and smoother operation.Cab D