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In Example 5.2-6, verify that the given transformation

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 15E Chapter 5.2

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 15E

Problem 15E

In Example 5.2-6, verify that the given transformation maps {(x1, x2) : 0 < x1 < 1, 0 < x2 < 1} onto {(z1, z2) : −∞ < z1 < ∞,−∞ < z2 < ∞}, except for a set of points that has probability 0. Hint: What is the image of vertical line segments?What is the image of horizontal line segments?

References Example 5.2-6

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Shakespeare Final Shakespeare – Titus Andronicus  Characters o Titus Andronicus – tragic hero, Roman general who returns to Rome from war with the Goths at the beginning of the play, b/c of his heroic deeds people want him to be emperor (but he does not), loyal to Rome & emperor Saturninus  Demands Tamora’s son Alarbus be killed as revenge for the deaths of some of his sons in battle  Grants his daughter to Saturninus  Turns other Goth prisoners over to Saturninus  Kills a son who tries to support Bassianus’ claim for Lavinia  At first, he refuses to bury this son in the family tomb  Duped by Aaron’s plot & the framing of his other sons  Assumes he can save his sons if he sacrifices his hand; gives the hand to Aaron, who brings the sons’ heads to Titus  Uses the sacrifice of his daughter to exact his revenge o Lavinia – Titus’s daughter, passive, given away in marriage to first Saturninus then Bassianus  Demetrius & Chiron rape her, cut out her tongue & her hands – mute as a result  Contrasted with Tamora (powerful, clever, wicked, cruel)  Killed by Titus b/c she has lost her honor, chastity, & virtue  Begs Tamora to put her to “present death” o Lucius – Titus’s son, only one to survive entire play, exiled from Rome  Goes to the Goths & raises an army to challenge Saturninus  Popular support of the Roman people, promise to return Rome to former greatness o Young Lucius – Titus’s grandson, Lucius’ son, survives the entire play, innocent bystander  Principal speaking scenes including reporting his aunt’s behavior and an address the the body of his grandfather o Quintus & Martius – Titus’s two sons who are framed for murder of Bassianus  Beheaded by Saturninus for the crime – this turns Titus against Saturninus  Titus tried to save them by sacrificing his hand o Mutius – Titus’s son, tries to prevent Lavinia & Saturninus’ marriage  Angry at betrayal of the emperor, killed by Titus  Mutineer, stands up to father’s wish of Lavinia marrying Saturninus & not Bassianus o Marcus Andronicus – Titus’s brother & a Roman tribune (elected official), advises Titus throughout the play, survives the entirety of the play, assures the Roman people along with Lucius that they will bring stability back to Rome  Tries to offer his hand to spare his brother’s hand  After Titus dies, helps the Titus’s son lead Rome or let Rome fall  Wants Titus to be emperor, but Titus gives the title to Saturninus o Publius –Marcus Andronicus’ son o Saturninus – oldest son of recently deceased Roman emperor, current emperor, Titus’s sons & Bassianus claim that he cannot marry Lavinia, angry at the Andronicus family, marries Tamora instead (she is lying to & manipulating him)  Killed for killing Titus  Mockingly gives Lavinia to Bassianus o Bassianus – Saturninus’ younger brother, does not allow Saturninus to marry Lavinia b/c she was betrothed to him, killed by Demetrius & Chiron (but Titus’s sons Quintus & Martius are framed for murder & executed)  Killed early in the play from a plot masterminded by Aaron o Tamora – queen of the Goths, brought as prisoner to Rome by Titus (who kills her son Alarbus & she swears revenge), wife to Saturninus,  Helps (Aaron, Demetrius, & Chiron) avenge Alarbus by raping & mutilating Lavinia, killing Quintus & Martius, & exiling Lucius o Alarbus – Tamora’s oldest son, killed by Titus to avenge his children’s deaths  “his entrals feed the sacrificing fire” o Demetrius & Chiron – Tamora’s sons, carry out Aaron & Tamora’s revenge plan against Titus, heartless & cruel, mock Lavinia after raping & disfiguring her  Told before their deaths that they will be baked into a pie for their mother o Aaron the Moor – Tamara’s secret lover & father of one of her children, African, villain  Abused by the Andronicus family, Demetrius & Chiron b/c he’s black  Arranges for Quintus & Martius to be framed for Saturninus’ murder  Encourages Demetrius & Chiron to attack Lavinia  Feels no regret when he is caught by Lucius except he wants to live longer to commit more crimes  Role is expanded from the source o Aemilius – Roman messenger who helps propel the plot along  Announces Lucius’ imminent arrival with armed Goths, sent to invite him to a truce meeting  At the end of the play, leads all to pronounce Lucius emperor o Clown – ordered to be killed by Saturninus, unaware that Titus’s supplication wrapped in a weapon will anger the Emperor o Nurse – killed by Aaron after expressing outrage at what Aaron has done  Earliest Shakespeare Tragedy – evidence that he collaborated with others  Several “givens” in comparison/contrast of Titus & Shakespeare’s later tragedies o Senecan values – early career o Later – developed tragedy beyond Titus level  Handout Questions o 1 & 2 – Hamlet & Othello vs. Titus  Aristotle tragedy – catharsis, self-recognition o 3 – Titus’s mental condition evolves later in the play  Hamlet pretends madness, extreme grief from loss of father  Titus does strange things – attributed to madness  Pretends to not know who his family is  Shakespeare sometimes lets the audience in on the ploy o 4 – Immature playwriting or brilliant scheme  changes orientation of the scene  Lavinia – Titus’s daughter, victim  Triggers in the play – touches you closely, like PTSD  Titus feels entitled to kill Tamora’s son to avenge his child’s rape & dismembering (trigger) o In turn, triggers revenge from Tamora  At the time Shakespeare wrote Titus, he also wrote The Rape of Lucrece which is mentioned in Titus  Normally - Vigilante justice – kill attacker  The Rape of Lucrece – 1 time crime is taken to state instead of person-person or family-family  Lavinia as victim/mute – crude scene when she names her rapist  She writes names with her arm stumps with a stick in the sand & points out a classical rape story  Victimized, uncomfortable stage time o 5 – last scene, ploy by Andronicus family who put up a case for their family to take over st  In the 1 scene – Titus comes home from war & is asked to name the next general  Titus has blind spots o 6 – divided by the consciousness of Aaron  Iago wanting to bring Othello down, Othello’s black power attitude  Titus – a mixed race child is brought to Aaron who refuses to get rid of the child  Family allegiance – even though the child is illegitimate  Caught – he pleads for child’s life, Lucius has to make the decision  Aaron – very important character, more than just the bad guy o 7 – Shakespeare’s development beyond Titus  Early - obvious allusions; later - uses literary style  Titus – not in control of allusions o 8 – Titus’s aside – tells audience & not Tamora that he is pretending madness  Hamlet – able to turn on his pretend madness o 9 – deaths o 10 – list of mistakes  Summary of article – Hammersmith too severely translated ‘hamartia’ to mean tragic virtue  Misguided in pursuits of what he thinks is right  Tragic pride over excessive pride  Father thinking he can make husband choice for his daughter – seen in several plays  Bassianus & Lavinia – she is given to Saturninus  Ending in problematic – Titus has to publicly kill (honor killing) to revenge his daughter  Cuts up Tamora’s sons & feeds them to her in a pie – taken straight from Seneca play  What becomes of Aaron’s child – not clear – Lucius agrees to let it live but may be faking it  Scene 1 o Titus is war hero, could be emperor  Romans & Goths are both barbaric o Goths defeated by Romans o Tamora’s 1 son sacrificed for Titus’s sons deaths o Goths – nebulous force o Lucius leaves to get on army to march against Rome  Titus kills Tamora’s sons & puts them in a pie to feed to Tamora  Titus plays along with people thinking he’s mad but tells audience in aside that he is not  Masque presentation – play figures have come to Titus’s window in costume o Tamora, Chiron, & Demetrius = Revenge, Rape, & Murder o Sympathize with Titus – really knows who they are  Aaron’s nationality – race is a big part of the play o Comes forward out of nowhere – on his own o Associated with Goths o Titus picture on pg. Plate 9 – Aaron to the side  Weirdness of Titus’s response to Lavinia’s rape – laughs b/c he can’t cry anymore – iron leader  Honor killing – raped woman killed o Private killings – rapist killed – private justice  Final scene – death, too rapid killings o Shakespeare’s early take on tragic endings o Titus kills Lavinia, Lavinia kills Saturninus  Psychotic Grief Illusion – Titus & Hamlet – so wrapped up in not getting over grief of a loss  Titus shoots messages in arrows to Empress – make sure Saturninus knows how he feels  Clown visits Titus – Clown goes to Saturninus & Tamora with note in Titus’s knife  Is Titus a full tragic hero  Sources o Seneca’s Thyestes o Ovid: for story of Philomel’s rape and revenge of Progne o Plutarch’s Parallel Lives of the Noble Greeks and Romans in a translation by North o A translation from the Italian of a chapbook, with Titus Andronicus in its title, not printed till the 18 century  Characteristics of the way Shakespeare uses allusions o Phrases in Latin o Characters’ awareness of plot of stories or events which involve the characters or persons: Virginius, Tereus, Philomel, Lucrece Shakespeare – Richard III  Characters o Duchess of York – Edward IV, Richard, Edmund, and Clarence’s mother, widow, protective of Elizabeth & her children, hates Richard o Richard – Duke of Gloucester  King, deformed, villain/evil  Killed by Richmond  First 3 Acts – Richard is called Duke of Gloucester; called King Richard later  Dictator who gets rid of his enemies – snapping behavior, turns on people, tyrant  Has a moment of guilt in his last soliloquy  Previously killed Henry VI in the tower  Animals associated with Richard: boar/hog, spider, toad, dog o Buckingham – Richard’s right hand man, character who most assists Richard in consolidating his power o King Edward IV – Richard & Clarence’s older brother o Queen Elizabeth – wife of King Edward IV, mother of 2 young princes & Dorset & Gray & Elizabeth, sister to Rivers, previously married to a Lancaster  Courted for her daughter Elizabeth, tells Richard he can’t have young Elizabeth after she asks her  Has her 2 young sons taken from her  Suspicious wife of Edward IV  Wooing scene – Edward IV’s brothers see him woo for the first time o Negative view of Queen Elizabeth o Young Elizabeth – Queen Elizabeth’s daughter, wanted by Richard, betrothed the Richmond at the end of the play, never appears in the play o The princes – sons of King Edward IV & Queen Elizabeth  Richard has the boys murdered by Tyrell in the Tower of London  Edward V – Richard’s nephew, Edward IV’s son o Clarence – Edward IV & Richard’s younger brother, has a son & daughter  Murderers tell him that his brother/Richard ordered his death o Dorset – son of Queen Elizabeth from previous marriage  Murdered by Richard o Gray - son of Queen Elizabeth from previous marriage  Murdered by Richard o Rivers – brother of Queen Elizabeth, flees & survives o Lady Anne – young widow of Prince Edward (son of former King Henry VI), wooed by Richard over the dead body of her father-in-law Henry VI, dies of sickness o Margaret – widow of late King Henry VI, mother of Prince Edward, prophetic  The only character to appear in all 4 plays in this series  Her son, Edward, was murdered by Richard and his brothers  She murdered Richard, Duke of York, & their father, who was king after Henry VI th  Also killed the 4 brother, young Edmund Earl of Rutland  Returns after her first curse to say “I told you so”  Curse all characters, they recall those curses later  Her action in the play is to prophecy & curse against those who have contributed to her downfall  Rivers, Hastings, Buckingham, Queen Elizabeth – make reference to Margaret o Ratcliffe & Catesby – Richard’s lackeys  Catesby – character who stays with Richard & will “help [him] to a horse.” o Tyrell – murderer, hired by Richard to kill the princes o Richmond – member of Lancaster family, gathers forces to challenge Richard for the throne, kills Richard, Christ-like warrior  Becomes Henry VII, father to Henry VIII  Has the last speech of the play o Hastings – lord who is loyal to the royal family, killed by Richard  Richard: “off with his head” o Lord Stanley – Richmond’s stepfather, secretly helps Richmond but pretends to be for Richard  Pledges loyalty to Richard, but after his son is taken hostage, secretly aligns with Richmond & is the character who offers Richmond the crown o Mayor of London – used by Richard in his plan to become king  Character who is fooled by the machinations of Richard & Buckingham o Vaughan – friend of Elizabeth, Dorset, Rivers, & Gray  Murdered by Richard with Dorset & Gray o Scrivener – makes copies of the death decrees & is aware of the rising death count  Places in the play o Tower of London – where Clarence & the princes were killed o Pomfrey - castle o Chertsey - castle o Tewskberry – famous battle, prior to play, where Margaret lost her son Edward o Bosworth Field – where Richard & Richmond are visited by ghosts  Sources o Tudor apologies o Senecan tragedy – avenging women o Sources in Hall & Holinshed derived from More  Similar o Anonymous True Tragedy of Richard III o Marlowe’s ambitious driven heroes – Tamberlaine, Faustus o Machiavelli’s The Prince, The Mirror for Magistrates o Medieval drama’s depiction of devils  Didactic religious drama depended upon the defeat/conversion of evil characters o Moral lessons placed side by side with the colorful presentation of evil  Hugh Richmond - Follows a medieval cycle o Wooing of Anne parallels Eve being tempted by the devil o Betrayal & murder of Clarence = Cain slaying Abel o Richard’s murder of nephews = Slaughter of the Innocents o Mater dolorosa o Richmond’s entry has parallels with New Testament salvation & noble warrior image of Christ  In histories & tragedies false motives are disguised sometimes with a flair  Shakespeare condenses history b/c he could leave things understood b/c of the audience he wrote for  Actual Title – The Tragedy of Richard III o Macbeth is a later version of Richard III o Will do anything to become king  Cohesiveness of the play o Biblical analogies – like Cain & Able  Buildup to Clarence’s murder – Richard builds plan to take over throne of England o House of York has just taken over  Wooing Scene – Richard woos Lady Anne – pg.775-756 o Richard is not suited to be romantic o Interrupts the body of Anne’s father in law (Henry VI) being buried in the family tomb  Richard killed Henry VI & his son (Edward) o Richard stops Anne & tells her why she needs a new husband o Anne agrees to marry him by the end of the scene  Vehemently against him at first – he killed her husband & father in law  Wants to reform/change Richard  Takes his word that he is changed by love  Power of Richard o Stichomythia – rapid fire one liners, argumentative  Pick up what one person says & reverse it  Common in wooing scenes  Shape of the Play – parallel wooing scenes nd o 2 – Richard asks for hand of young Elizabeth (his niece) by wooing her mother, Queen Elizabeth  Ends with no conclusion b/c Queen Elizabeth says she has to ask her daughter’s opinion  Richard thinks he has won Queen Elizabeth over – crack in his facade  Act 1, scene 4 o Hire people to kill Clarence & blame someone else  Richard contrives to make it look like King Edward IV ordered the death of Clarence  Frame the death on a misunderstanding of orders o Clarence & Richard are married to sisters (Neville family)  Richard wants to kill family members close to the throne o Even kill of/ get rid of Clarence’s sons o Get rid of sons of Edward IV – illegitimate father & sons o Edward IV will die of sickness o Make it look like he’s a good guy  Edward IV dies – Richard is protector of his son’s o Nephews are ahead of Richard for the throne o He gets Buckingham to do the dirty work  Coronation scene – Richard becomes King, orders nephews’ death o Richard bypasses the princes o Buckingham calls Richard king early by accident o Excuse for execution: they are bastards & not legitimate heirs  Richard has no biological heir – tells people Anne is sick so he can get a wife to give him an heir  Anne says that Richard is sleepless & keeps her up at night – dreams o Richard wants to marry his niece young Elizabeth  She actually marries Richmond (Henry VII) in the end  Hastings raises objection & pisses Richard off – shows how mean he can be o Richard: “Off with his head” o Richard attacks Hastings  Parallel to Buckingham (helps Richard consolidate power)  Strangles the princes, but hesitates when Richard gives the orders  Margaret – 2 scenes – widow of Henry VI o Act 1, scene 3 – prophecy  Supposed to be exiled to France  Vehemently against line of Tudors  Vs. Act 4, scene 4 – I told you so, should have listened o Shows how bad Richard is o Prophecy are recalled by people who become Richard’s victims o Act 4, scene 4  Rhetorically patterned, listing  Margaret precursor for how witches function  Act 4, scene 4 o Margaret watches destruction happen o Grieving mothers o Line 40 – people Richard has killed o Line 49 – Richard has been deformed since he was in the womb, blackening of his character o Line 124 – credit Margaret, wants to be taught how to curse enemies o Encouragement to curse Richard – full of bad things to say o Stichomythia – Richard asking for Queen Elizabeth’s daughter o Line 431 – Richard’s 1-line soliloquy o Richard thinking about future (new wife & kids) – realizes he has to act faster  Ghost scene - Sequence of ghosts appear to Richard to curse him & bring good news to Richmond o People who appear: King Henry VI, Lady Anne, George, Vaughan, Edward Warwick, Prince Edward/Edward V, Richard Duke of York, Buckingham, Hastings, Grey, Rivers  Act 5, scene 3 – sequence of Richard’s victims o Hastings dies before princes o We don’t see Anne die o Buckingham gives speech on the way to hanging  Last action of the play is Richmond’s promise to consolidate the houses of York & Lancaster & bring an end to civil wars  Dreams o Clarence dreams he is killed by Richard o Clarence dreams that Richard pushes him overboard o Stanley sends a messenger to Hastings that he has dreamt of the boar/Richard o Lady Anne says she has not slept since marrying Richard b/c of his dreaming o Richard & Richmond are visited by the ghosts of Richard’s victims  Lady Anne references to a creature – basilisk o Name she calls her husband by Plantagenet (people associated with Henry VI)  Difference between 1 executioner & 2 ndexecutioner o 1 feels remorse; 2 ndcalls 1 a coward  Henry wants Lord Stanley’s son to stay behind o Fears that Stanley will go over to Richmond’s side o 1 time we see Stanley is with Richmond  Duchess of York vs. Margaret o Duchess – mother to Clarence, Richard, & Edward IV; widow of Richard, Duke of York  Matriarch still connected to power o Margaret – widow to past king, disconnected  Richard killed Henry, harsh to Richard  Deaths by Richard o “Off with his head!” – Lord Hastings o “I wish the bastards dead.” – Prince Richard & Edward o “But sirs, be sudden in the execution . . . do not hear him plead.” - George o “Hath any well-advised friend proclaime’d/ Reward to him that brings the traitor in” - Buckingham o Give out that __ is sick, and like to die.” - Anne o “The son of Clarence have I put up close,/ His daughter have I meanly match’d in marriage.” – Edward Plantagenet & Margaret Plantagenet  Soliloquies o 1) Introduces War of the Roses background info & Richard as deformed villain o 2) Richard has spoken to Clarence about going to the tower, Richard reveals his plot to kill Clarence  Richard – brief, effective, full plot revealed later o 3) blame Clarence’s death on King Edward, marry Anne scheme/plot, arrogance & selfish motive revealed later o 4) mocking self-importance, ‘look what I got away with’ o 5) Queen Margaret cursed everyone, nothing would be happening if he wasn’t doing it, plan to frame Queen Elizabeth & her allies  Like Hamlet’s soliloquy – announcing plots o 7) 2nd murderer – total regret, biblical allusion to Pilot b/c senseless murder of Clarence o 8) 1 murderer – sneering at 2 ndmurderer for being hesitant  foreshadows that someone will realize that Richard had him kill Clarence o 9) Scrivener has indictment for Hastings  People turn their heads b/c they’re afraid of Richard  Shakespeare’s histories – present regal characters & commoners comment on action  Scrivener – commoner, copies official orders  Speeches that end in rhyming couplets o 10) plan to marry young Elizabeth, loosing allies, intelligent & ruthless, deep in blood o 11) Richard’s complete consumption of power o 12) killers are remorseful, Richmond is interested in Elizabeth but Richard needs to marry her to right his wrongs  Tyrell didn’t complete the murder – Villains he hired to murder feel guilty  Pure language, slaughter of innocence o 13) looking back & forward, “a jolly thriving warrior,” bridge to next wooing, Richmond is rival wooer o 14) bragging that everyone is getting what they deserve, mourning lost men  Next scene – power from listening when they don’t know she’s there  Tells audience ‘told you so’ first o 15) King Richard’s true reaction to Queen Elizabeth, contrast to soliloquy 4, rapid fire conversation of bad military news o 16) Psychological high point – ghosts, prayer-like, confident tone, Richmond is reinforced as good guy o In between 16 & 17 is significant – realize Richard’s downfall o 17) real pangs of conscience, Richmond is being given good words is part of Richard’s nightmare – fears Richmond is taking the throne Shakespeare – As You Like It  Characters o Duke Senior – father of Rosalind & rightful ruler of Dukedom, banished by his brother Duke Frederick, lives in exile in Forest of Ardenne with loyal men (including Amiens & Jacques), kind & fair  Befriends Orlando b/c knows Orlando’s father o Jacques – accompanies Duke Senior into exile, stock figure, decides to become monk, cynical character  Lectures Touchstone about marrying quickly & regretting it & on marrying a loose woman  Leaves Corin without a function in the play  Critical of those in the forest who kill deer for sport or meat  Approves of what is reported that Frederick has done to change his life, vows to seek him out o Lord Amiens – goes into exile with Duke Senior, loves to sing o Rosalind – daughter of Duke Senior, disguises as Ganymede, loves Orlando  Dresses as man for protection & to not be discovered by Orlando  Gets Orlando to practice wooing her to check the match & determine if he’s a worthy suitor, power to choose her own mater  Gives the Epilogue – makes reference to “her” status as a boy actor o Duke Frederick – Duke Senior’s brother, usurper of throne, banishes Duke Senior & Rosalind, meets old religious man in the woods & changes his ways, becomes a monk & returns throne to Duke Senior o Celia – daughter to Duke Frederick, Rosalind’s friend & cousin, follows Rosalind into exile, disguises herself as shepherdess named Aliena, marries Oliver, agrees to marry before Rosalind o Sir Rowland de Bois – Orlando & Oliver’s father, friend to Duke Senior, enemy to Duke Frederick o Oliver – Sir Rowland de Bois’ oldest son, inheritor of de Bois estate, doesn’t let Orlando get a gentleman’s education, hates Orlando, becomes a better person after Orlando saves him, loves Celia  Meets Celia when he is bringing Orlando’s bloody handkerchief to Ganymede/Rosalind; love at first sight o Jacque – middle son to Rowland de Bois, plot device, mentioned briefly in the beginning of the play as off at school, has a single scene o Orlando – youngest son of Sir Rowland de Bois, Oliver’s brother, wins battle against Charles, cares for Adam in the forest, saves Oliver from lioness, loves Rosalind  Angry at Oliver for depriving him of what he is due  Goes to the woods b/c Adam warns him of people trying to burn the house down o Adam – elderly former servant of Sir Rowland de Bois, accompanies Orlando into exile & funds the journey with his life savings  Cannot continue in the forest with Orlando b/c he is famished & unable to go on o Phoebe – young & suffering shepherd, ignores Silvius, falls in love with Ganymede/Rosalind, tricked by Rosalind into marrying Silvius o Charles – professional wrestler in Duke Frederick’s court, asks Oliver to convince Orlando to not fight him  Has 2 single entrances/scenes in the play o Corin – shepherd, attempts to council Silvius about love o Touchstone – court clown, accompanies Rosalind & Celia, echoes with innuendos  Gives very sophisticated lecture on lies 7 times removed  Steals Audrey from William  Meets Jacques in the forest  Accompanies Rosalind & Celia out of his element into the forest, being comic for Duke Senior brings him back into his element  Makes fun of Corin’s sheep-handling logic & reasoning by showing how useless it would be at court o Audrey – simpleminded goatherd, agrees to marry Touchstone o William – young country boy, loves Audrey, does not defend his right to marry Audrey o Oliver Martext – marries characters, fudges things o Hymen – god of marriages, supposedly delivers Rosalind to Orlando  Appears to bless the wedding but does not speak  Parody of pastoral romance, middle Shakespeare comedy o Pastoral concept – can recover your senses & live in laid back way o Written during 2 literary fashions: pastoral & Satire  Pastoral – glorification of supposedly “pure” country over the “wicked” city or court  Satire – Elizabethan satire was a criticism of contemporary manners & morals  Background o Source – battle scene interrupts marriages o Plot take from a pastoral romance – Thomas Lodge’s Rosalynde – published in 1590  Pastoral romance – long prose tale of love & adventure in which shepherds woo shepherdess in witty & sophisticated language  Developed the love pairs with lengthy courtship & love songs  Shakespeare – love at first sight instinct  More battles & deaths in the source than in Shakespeare  Shakespeare added characters: William, Audrey, Jaques, & Touchstone  Shakespeare – sudden change in evil characters o Court Fool  Jacques is impressed by Touchstone & wants to become a court fool  Can criticize whoever without fear of retaliation  Very often the fool is one of the sanest people in the play o Love convention – Petrarchan Love (celebrated in his love sonnets)  The lady is nobler & purer than her love. Lover has to prove worthy of his love.  The lover wrote love poems to the lady to describe how much her love was making him suffer  Pairs of characters end up married; agenda – celebration of multiple matings  Neither Le Beau nor Touchstone are present when Celia & Rosalind scheme to take the fool with them into the forest  Characters sing: Touchstone, Lord Amiens, Hymen, Pages  “All the world’s a stage” – speech about 7 stages of man o Building up to honorific way to introduce Adam o Welcome Adam with honor & feed him o Entrance of Adam undercuts what Jacques says  “sons” = without/lacking, Adam is restored (no more lines after revival)  Rosalind – in control of the matchmaking, promises Orlando his love will appear o Ready to give up her disguise but wants to remain in control of the reveal o Premonition of conditions that will be met – “if” statements (reverberation of As You Like It concept)  Rosalind makes promises that will be kept if conditions are met o Gives the same line to her father & her lover o References magicians in the woods – example of Shakespeare’s quick solution to plot hole  Act 5 o Counterfeit scene  Oliver brings Orlando’s bloody handkerchief to Ganymede/Rosalind  Rosalind faints at the sight of the blood, says it is counterfeit  Aliena/Celia falls in love with Oliver at first sight  Oliver wants to stay in the woods to live & die a shepherd with Aliena  Orlando is remorseful that Orlando found love first  5.2 – bitter think to look at happiness through another man’s eyes o 5.3 - Silvius explains what love is; Orlando slips & says “you” to Ganymede/Rosalind o 5.4 - Duke Senior says Ganymede reminds him of Rosalind o Hymen’s speech – brings Rosalind to the wedding o Jacque de Bois’ speech – announces that Duke Frederick has decided to become a monk & return the crown to Duke Senior Shakespeare – Twelfth Night  Characters o Orsino/Duke – mates with Viola, nobleman in Illyria, originally in love with Olivia  Knows the father of Viola & Sebastian o Valentine – in Orsino’s court, 1 of the carriers of letter to Olivia o Viola – Sebastian’s twin, disguises as man named Cesario, washes up on shores of Illyria after shipwreck, becomes Orsino’s page, falls in love with Orsino  Tries to get Olivia to back off being interested in her as Cesario  1 to expect that the other twin is alive  Promises to change clothes but can’t b/c another has the garments  Soliloquy – figures out what Malvolio means after he “returns” a ring o Sebastian – Viola’s twin lost in the shipwreck, arrives in Illyria with friend Antonio, people in Illyria claim to know him & Olivia wants to marry him  Friendship with Antonio is a mystery  Bloodies Sir Andrew & Sir Toby – but they think by Cesario  Soliloquy – thinks he is in a dream but embraces the state of being idolized o Antonio – rescues Sebastian, loves Sebastian & cares for him on the journey to Illyria o Olivia – in love with Cesario but ends up with Sebastian, wealthy noble or Illyria, courted by Orsino & Sir Andrew, mourning her brother & father, claims she will not marry for 7 years  Sends Malvolio with a ring to Cesario  Sees Sebastian, thinks its Cesario – her miracle seems to come true b/c Sebastian is clueless; sends for a priest, confused about which twin she married when they are on stage together  Soliloquy – speaks 2 couplets at end of scene to confirm her infatuation o Malvolio – head servant in Olivia’s household, cynical, others turn the tables on him for being too strict, too controlling, prude, puritan-like  Shows up in yellow garments with crossed garters b/c of the planted letter  Soliloquy – in prose he presumes Olivia likes his new look & attitude o Fabian – in Olivia’s household, wants to see Malvolio plot, scolded for arranging a bear baiting in Olivia’s home  Announces the success of Maria pulling off the trick that made Toby propose to Maria & turns the letter over to be read o Sir Toby – in Olivia’s household, Olivia’s uncle, part of Malvolio plot, mates with Maria, Olivia disapproves of his drinking & joking, sings b/c music supports that he is in love o Maria – gentlewoman in Olivia’s household, far back interest in Malvolio being put in his place  Marries Sir Toby in return for how cleverly she tricked Malvolio o Sir Andrew Augecheek - in Olivia’s household, friend of Sir Toby, comes with money, like Roderigo in Othello, promised access to Olivia o Feste/Clown - in Olivia’s household, sings for entertainment, suggests you can pay him for performing & will do more if you pay more, pure fool, given chance to sing, concluder of dialogue  Sir Topas a Cleric (disguise) – a priest that pretends to examine Malvolio & determines him to be insane  Soliloquy – sings to end the play o Priest – sent for by Olivia for her marriage o Captain – friend & savior to Viola; like Antonio is to Sebastian  C.L. Barber famously labeled this as Festive Comedy  Harold Bloom claims the play is dark & good b/c it doesn’t fit in any genre o Viola seems second only to Rosalind in his rating of female characters along his ranking of fully rounded humans rather than dramatic types  2ndtitle – What You Will – more accurate to the play than Twelfth Night o Twelfth Night as a festive holiday celebration  Feste/fool – points to festivity  12 days of Christmas were common performance dates for royalty  Nothing in the play references the title  Misrule & sorting out confusion is typical for holiday festivity  Festive includes taking on a role that violates one’s understood place in society  Characters in Shakespeare vs. Source o Main English source: Barnabe Riche’s novella of Apolonius & Silla, which has origins in Italian plots o Shakespeare – brother comes in for resolution, Apolonius & Silla are main characters o Not original to Shakespeare - Female disguised as male & mistaken, brother as resolution to disguise plot o Ancient Greek theory of four humours  Popularized & ironized by such playwrights as Ben Jonson  Aspects of the theory of humours may be tied to Shakespeare’s participation in the War of the Theatres or Poetomachia  Malvolio is akin to Jacques, but how he participates in the main  Feste is akin to Touchstone  2.5 - Entrapment of Malvolio – other characters in Olivia’s court play a trick on Malvolio o Characters in on the joke – Maria, Toby, Feste, Andrew, Fabian o Maria volunteers to write a letter in Olivia’s hand & dresses like Olivia o Malvolio falls for the letter left out for him to find – characters hiding to watch are Fabian, Sir Toby, & Sir Andrew  The letter tells him to dress funky  Malvolio is so engrossed in the letter, he has no idea others are on stage o Olivia is stupefied b/c she’s not in on the joke, thinks Malvolio is mad/sick o Malvolio misunderstands when Olivia tells him to go to bed – he thinks sex o Malvolio exposes the trick, Olivia feels sorry for him & punishes her servants  Last line – revenge, deserves to air grievances o Sir Toby hears Malvolio simulate a scolding or reprimanding of him for drinking  Always 1 character or more left out of comic resolution o Don Jon in Much Ado is sent to jail; Jacques in As You Like It choose to withdraw; Shylock in Merchant of Venice is forced to convert to Christianity  Dark humor – Malvolio’s torment, Sir Toby’s punishment  Olivia & Viola both lost brothers in a sense o Olivia keeps a household that preserved her mourning for her brother & father  ‘Woo for me’ – Olivia falls in love with Cesario as messenger for Orsino; Orsino has not made headway on his own & needed help  Act 1 o Shipwreck – 1 twin saved another, important but kind of corny  Subplot o What happens in Olivia’s household, servants ignore Malvolio

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Chapter 5.2, Problem 15E is Solved
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Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

Since the solution to 15E from 5.2 chapter was answered, more than 329 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. The answer to “In Example 5.2-6, verify that the given transformation maps {(x1, x2) : 0 < x1 < 1, 0 < x2 < 1} onto {(z1, z2) : ?? < z1 < ?,?? < z2 < ?}, except for a set of points that has probability 0. Hint: What is the image of vertical line segments?What is the image of horizontal line segments?References Example 5.2-6” is broken down into a number of easy to follow steps, and 63 words. This full solution covers the following key subjects: Example, segments, line, image, onto. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The full step-by-step solution to problem: 15E from chapter: 5.2 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM.

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In Example 5.2-6, verify that the given transformation