In Exercises 5.13 and 5.31, the joint density function of Y1 and Y2 was given by
Are the random variables Y1 and Y2 independent?
The joint density function of Y1 and Y2 is given by
In Exercise 5.13, the joint density function of Y1 and Y2 is given by
a Show that the marginal density of Y1 is a beta density with α = 2 and β = 4.
b Derive the marginal density of Y2.
c Derive the conditional density of Y2 given Y1 = y1.
d Find P(Y2 > 0|Y1 = .75).
History Class Notes March 30, 2013 Quiz #13 due Thursday 1960s ** IMPORTANT EVENT in the 1950s Kitchen Debate 7/24/59 - Vice President Nixon (President Eisenhower) and Soviet Premier Nikiti Khrushchev met at American National Exhibit Moscow - Nikki opposes Stalon and a new kind of leader - The 2 leaders in the Cold war have open exchange about the merit system o Tries to build his image over seas o Makes history- goes to Moscow in 1959 o He shows off how American technology has improved in the post WWI era - Discussed merits of capitalist vs communist systems in the context of postwar prosperity - Cultural exchange in the midst of the Cold War - Called the “Kitchen debate” because that were the 2 leader were talking and that’s where the TV was set up to catch them talking o It becomes standard to have a TV in their home They will have a different type of access of the news ***Important because this is even being able to happen during the Cold War o See a brief moment of diplomacy o Civil encounter o Diplomatic and Nixon is coming off to be a candidate to run for President President Eisenhower almost ended the Cold War in the 1960s Francis Gary Powers 5/1/60 - Paris Summit May 1960- possible end to the Cold War during Eisenhower administration - Meeting not popular among hardline anticommunists - U-2 spy planes used by CIA in 1950s to collect info on Soviet missiles - Powers flight 5/1/60 shot down and captured alive; cover up prolongs Cold war and destroys trust between countries 1960 Presidential Election **IMPORTANT because first election to be televised - Before this a citizen did not know what the candidates looked like John F. Kennedy (Democratic Party) - Senator from Massachusetts - New Frontier approach - Catholic – important to address o Question: is the Pope really running for President o Kennedy says that he believes in the separation of the church and state - From wealthy family - Emphasis for his 5 o’clock shadow Richard M. Nixon (Republican Party) - Eisenhower VP - Experienced diplomat - From working class family 88% of Americans had TVs 74 million tuned in on TV or by radio Role of lighting and makeup for TV performance Difference between TV watchers and radio listeners No TV debates until 1976 due to this outcome Close election of 1960 Radio- thought Nixon wins the 1 debate TV- thought Kennedy won the 1 debate **the election was really close - Kennedy won by 1/10 of 1%h Bay of Pigs 4/17/61 - Fidel Castro overthrows Batista dictatorship January 1959, nationalizes sugar industry - CIA plan: assault landing in Cuba to overthrow Castro; utilize anti- Castro Cuban exiles to disguise US involvement - Ends in disaster when plans are leaked and Castro is ready Cuban Missile Crisis, 1962 - Operation Mongoose- CIA still wants to Castro ‘removed’ - Cubans look to Soviet Union for defensive arms - Soviets interested in nuclear weapons in Western Hemisphere- shipped in missiles by boat to Cuba - JFK addresses US on TV to explain situation; presents ultimatum to Soviet Union- it works Dallas, Texas November 22, 1963 - A parade in Texas because Texans were not a fan of Kennedy - People were accusing him of treason o Many people actually showed up o President and wife in a car, Governor of Texas in car ahead o Shots were fired Kennedy was hit Governor was hit o After this event you know where you were, and wondering what is happened, in fear o In the middle of the Cold war while the President was shot and killed Death of a president 11/22/63 1964 Election Johnson (democratic) - Wins overwhelmingly - Will continue Kennedys’ administration Goldwater (republican) *******The Bible belt goes Republican - Change starts taking place Conservative Economic Political Thought th Product of the 20 century- saw it in the Great Depression (opposition of the New Deal) - Crisis of the Great Depression- would the New Deal help or harm Americans and the American economic system - Conservative economists: regulation will stifle growth and prosperity - Tension with the Soviet Union before and after World War II o Communist system fundamentally incompatible with American free trade o Leads to staunch commitment to the Cold War and defeat of USSR o Communism also inherently unfriendly to Christian beliefs because of centrality of the state o Anti-communism seen as important political stance Expressions of Conservative Politics Support of Senator McCarthy - Participation in organizations designed to investigate communism in local organizations - Opposition to United Nations - Fusions of political and religious messages o Revivals: Bill Graham evangelicalism connects anticommunism with being saved; communism is ‘evil’ o ‘Under God’ added to the Pledge of Allegiance, 1953 o “In God We Trust’ added to coins, 1957 - Religion is a way to keep people in control The Sunbelt Region (States in the lower borders of the US: SC, GA, AL, LS, TX, CA, NM) - Areas in the South and Southwest and West benefit from post-war industry in oil, defense, and manufacturing - Defensive budget = 62% Federal Budget in 1960s - Major military bases and Cold War industry sites becomes highly anticommunist; burgeoning area for modern conservatism - Opposition to JKF- to ‘soft’ on communism - Breaks up New Deal coalition 1964 – Barry Goldwater (1 Conservative to win Republican) - Strong anti-communist - “Mister conservative” Republican Senator from Arizona - He believes in small governemtn and it in not the right of the federal government to involve themselves in civil rights in the state - Anticommunist, supported use of nuclear weapons - Large government is to blame for moral problems - Opposed Civil Rights Act of 1964 as a violation of states right *****why the bible belt starts to turn Republican Phyllis Schlafly - Support Barry Goldwater campaign in A Choice Not an Echo o Criticized ‘Me too’ Republicans like Eisenhower for not standing up for conservative principles o Chiefly concerned with anticommunist politics o Influential in Goldwater’s Republican nomination Goldwater’s opponents - Question the limits of the Right’s agenda - Supporters tap into voter fears that the country is not being governed by conservatives Election of 1964 **when the Bible belt goes Republican - The voters that vote for Goldwater opposed the Civil Rights movement (the South) - Johnson won election by a landslide o Gained 90.6% of the electoral vote o Gained 51% of the popular vote