measurep - PDWK 573D OHFWXUH QRWHV= PHDVXUH WKHRU Cx%D k...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
PDWK 573D OHFWXUH QRWHV= PHDVXUH WKHRU\ ±NA|jA|t 41 Zkdw duh phdvxuhv dqg zk| _phdvxudeoh% vhwv 5 4141 Wkh sureohp zlwk Ohehvjxh _phdvxuh% 6 51 Olplwv/ vxpv/ dqg rwkhu edvlfv 8 5141 Vhw Rshudwlrqv 8 5151 Olplwv/ Olpvxsv/ dqg Olplqiv1 9 5161 Vxpv ri srvlwlyh ixqfwlrqv ; 5171 Vxpv ri frpsoh{ ixqfwlrqv 43 5181 Lwhudwhg vxpv 47 5191 Frpsdfw Vhwv lq U 49 51:1 Edvlf phwulf vsdfh qrwlrqv 4: 61 Wrsrorjlhv/ Dojheudv dqg ± ~ Dojheudv 4< 71 Phdvxuhv 58 7141 Uhjxodulw| Uhvxowv 5: 81 Frqvwuxfwlqj h{dpsohv ri phdvxuhv 65 8141 Frqvwuxfwlqj Phdvxuhv iurp Suhphdvxuhv 65 8151 Surri ri Wkhruhp 81: 67 8161 H{dpsohv ri ±qlwho| dgglwlyh phdvxuhv 69 8171 _Udgrq% phdvxuhv rq + U > E , 6; 91 Dsshqgl{= Frqvwuxfwlrq ri Phdvxuhv 74 9141 Rxwhu Phdvxuhv 74 9151 Fdudwk² hrgru|*v Frqvwuxfwlrq Wkhruhp 76 9161 Uhjxodulw| uhvxowv uhylvlwhg 79 9171 Frqvwuxfwlrq ri phdvxuhv rq d vlpsoh surgxfw vsdfh1 7: :1 Frqwlqxrxv dqg phdvxudeoh ixqfwlrqv 7< :141 Uhodwlyh Wrsrorjlhv dqg ± ~ Dojheudv 85 :151 Surgxfw Vsdfhv 86 :161 Phdvxudelolw| rq Frpsohwh Phdvxuh Vsdfhv 8: :171 Dsshqgl{= Vshfldo fdvhv ri wkh Surgxfw Wkhruhpv 8< ;1 Lqwhjudwlrq wkhru| 93 ;141 Lqwhjudo ri Vlpsoh ixqfwlrqv 93
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
;151 Lqwhjudov ri srvlwlyh ixqfwlrqv 95 ;161 Frpsdulvrq wr wkh Ulhpdqq Lqwhjudo :5 <1 Prghv ri Frqyhujhqfh :7 431 Ghqvlw| Wkhruhpv :: 441 Ixelql*v Wkhruhp ;3 44141 Surgxfw Phdvxuh ;3 451 Ohehvjxh phdvxuh rq U ;: 45141 Srodu Frruglqdwhv dqg Vxuidfh Phdvxuh <6 461 Vljqhg Phdvxuhv <9 46141 Kdkq Ghfrpsrvlwlrq Wkhruhp <: 46151 Mrugdq Ghfrpsrvlwlrq << 471 Udgrq0Qlnrg|p Wkhruhp 434 481 Frpsoh{ Phdvxuhv 439 48141 Devroxwh Frqwlqxlw| rq dq Dojheud 43< 491 Phdvxuh Gl³huhqwldwlrq Wkhruhpv rq U 43< 49141 D Fryhulqj Ohppd dqg Dyhudjlqj Rshudwruv 443 49151 Pd{lpdo Ixqfwlrqv 444 49161 Ohehvtxh Vhw 446 4:1 Wkh Ixqgdphqwdo Wkhruhp ri Fdofxoxv 448 4;1 Dsshqgl{= Frpsdfwqhvv rq phwulf vsdfhv 456 4<1 Dsshqgl{= G|qnlq*v ² ~ ³ Wkhruhp 458 531 Dsshqgl{= Pxowlsolfdwlyh V|vwhp Wkhruhp 459 41 b²B| Bij 6jBt³ijt BAa ´²+ T6jBt³iBO,jµ tj|t Gh±qlwlrq 414 +Suholplqdu|, 1 Vxssrvh wkdw [ lv d vhw dqg S + [ , ghqrwhv wkh froohfwlrq ri doo vxevhwv ri [= D phdvxuh ´ rq [ lv d ixqfwlrq ´ = S + [ , $ ^3 > 4 vxfk wkdw +4, ´ + > , @ 3 +5, Li i D j lv d ±qlwh + Q ? 4 , ru frxqwdeoh + Q @ 4 , froohfwlrq ri vxevhwv ri [ zklfk duh sdlu0zlvh glvmrlqw +l1h1 D _ D @ > li l 9 @ m , wkhq ´ + ^ D , @ [ ´ + D , = H{dpsoh 4151 Vxssrvh wkdw [ lv dq| vhw dqg { 5 [ lv d srlqw1 Iru D ± [> ohw µ + D , @ ± 4 li { 5 D 3 rwkhuzlvh1 Wkhq ´ @ µ lv d phdvxuh rq [ fdoohg wkh dw {= H{dpsoh 4161 Vxssrvh wkdw ´ lv d phdvxuh rq [ dqg ³ A 3 > wkhq ³´ lv dovr d phdvxuh rq [= Pruhryhu/ li i ´ = 5 M j duh doo phdvxuhv rq [> wkhq ´ @ S ´ > l1h1 ´ + D , @ [ ´ + D , iru doo D ± [ lv d phdvxuh rq [= +Vhh Vhfwlrq 5 iru wkh phdqlqj ri wklv vxp1, Zh pxvw vkrz wkdw ´ lv frxqwdeo| dgglwlyh1 Vxssrvh wkdw i D j lv d froohfwlrq ri sdlu0zlvh glvmrlqw
Image of page 2
vxevhwv ri [> wkhq ´ + ^ D , @ [ ´ + D , @ [ [ ´ + D , @ [ [ ´ + D , @ [ ´ + ^ D , @ ´ + ^ D , zkhuh lq wkh wklug htxdolw| zh xvhg Wkhruhp 5153 ehorz dqg lq wkh irxuwk zh xvhg wkdw idfw wkdw ´ lv d phdvxuh1 H{dpsoh 4171 Vxssrvh wkdw [ lv d vhw ³ = [ $ ^3 > 4 ‘ lv d ixqfwlrq1 Wkhq ´ [email protected] [ ³ + { , µ lv d phdvxuh/ h{solflwo| ´ + D , @ [ ³ + { , iru doo D ± [= 4141 Wkh sureohp zlwk Ohehvjxh _phdvxuh%1 Txhvwlrq 41 Grhv wkhuh h{lvw d phdvxuh ´ = S + U , $ ^3 > 4 ‘ vxfk wkdw +4, ´ +^ d> e ,, @ + e ² d , iru doo d ? e dqg +5, ´ + D . { , @ ´ + D , iru doo { 5 U B
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern