course notes for unit 6 of the udacity course st101 introduction to statistics
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
1/23
QZ848 Umgz 9? Re`reqqgcm
Acmzemzq?Re`reqqgcm
Acrrelhzgcm
Fcmzw Nhll Trcblef .Ctzgcmhl'
Hmqperq
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
2/23
Re`reqqgcm
Wcu qnculj refefber ircf zne yerw be`gmmgm` ci zngq acurqe znhz pe ahm nhye jhzh
qezq pgzn fcre znhm cme jgfemqgcm- Icr e~hftle, zne qge ci h ncuqe relhzgye zc gzq
trgae?
Gm zne igrqz umgz pe qhp jgiieremz phwq ci treqemzgm` zne jhzh, lgke qahzzer&tlczq cr bhr
anhrzq, buz pe jgjmz lcck hz pnhz fg`nz be zncu`nz ci hq zne Nclw @rhgl ci qzhzgqzgaq,
igzzgm` h lgme zc zne jhzh tcgmzq?
Bw zne emj ci zngq umgz wcu pgll be hble zc igz h lgme zc jhzh tcgmzq lgke zneqe, hmj wcu
pgll eyem be hble zc qzhze pnhz zne reqgjuhl errcr gq gm znhz igz- Zngq pgll hllcp wcu mcz
cmlw zc umjerqzhmj zne jhzh, buz hlqc zc fhke trejgazgcmq hbcuz tcgmzq znhz wcu nhye
meyer qeem beicre-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
3/23
Lgmeq
Ncp jc pe qteagiw h lgme3 Pell, quttcqe pe nhye h ncrgcmzhl h~gq, ~, hmj h yerzgahl
h~gq, w- H qzrhg`nz lgme gq acffcmlw jeqargbej bw h iumazgcmhl relhzgcmqngt bezpeem ~
hmj w ci zne icrf?
hb~w
Acmqgjer zne lgme jeqargbej bw zne iumazgcm w 6 2~-
Gi ~ 6 4 znem w 6 4- Zngq fehmq znhz zne lgme fuqz c znrcu`n zne crg`gm- Gi ~ 6 2 znem
w 6 :- Pe mcp nhye zpc tcgmzq hmj pe ahm jrhp cur lgme?
Tgak zne Lgme Xug
Pnhz hbcuz zne lgme, w 6 &~ +: g-e- pnere b 6 8 hmj h 6 :- Pngan ci zneqe lgmeq beqz
fhzaneq zngq iumazgcm3
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
4/23
Igmj Aceiigagemzq Xug
Pnhz hre zne aceiigagemzq h hmj b icr zne lgme qncpm belcp?
hb~w
Lgmehr Re`reqqgcm
Gi pe nhye 2&jgfemqgcmhl jhzh, icr e~hftle zne h`e ci h terqcm hmj znhz terqcmq
gmacfe, lgmehr re`reqqgcm gq h zeanmgxue icr zrwgm` zc igz h lgme znhz beqz jeqargbeq znhz
jhzh?
Gm lgmehr re`reqqgcm pe hre `gyem jhzh .nhygm` fcre znhm 8&jgfemqgcm', hmj pe
hzzeftz zc igmj zne beqz lgme zc igz zne jhzh- Zc tuz zngq jgiieremzlw, pe hre zrwgm` zc
gjemzgiw zne thrhfezerq h hmj b icr zne iumazgcm?
hb~w
Pe hre zrwgm` zc igmj zne lgme znhz gq zne beqz&igz zc cur jhzh, hmj zne pcrj beqz gq
gmzereqzgm` gm zngq acmze~z- Cbygcuqlw gz gq gftcqqgble zc jrhp h qzrhg`nz lgme znhz
thqqeq znrcu`n eyerw tcgmz gm zngq jhzh qez?
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Zngq gq pnhz gq kmcpm hq mcm&lgmehr jhzh & zne jhzh tcgmzq `c ut hmj jcpm- Jhzh
cizem lcckq lgke zngq, eyem pnem zne relhzgcmqngt bezpeem ~ hmj w gq lgmehr- Zngq gq
beahuqe znere gq uquhllw pnhz gq kmcpm hq mcgqe gm zne jhzh- Mcgqe gq h rhmjcf
elefemz gm zne jhzh znhz pe ahmmcz e~tlhgm-
Gm zrwgm` zc igmj zne beqz&igz zc zne jhzh, pe hre zrwgm` zc igmj h lgme znhz fgmgfgqeqzne jgiieremaeq bezpeem zne jhzh tcgmzq hmj zne lgme gm zne w&jgreazgcm?
Zne rehqcm icr zngq gq znhz pe hre hqqufgm` znhz cur jhzh requlzq ircf qcfe umkmcpm
lgmehr iumazgcm tluq mcgqe?
mcgqehb~w
Gi zne mcgqe gq hqqufej zc be @huqqghm, znem fgmgfgqgm` zne xuhjrhzga jeyghzgcm
bezpeem zne jhzh tcgmzq hmj zne lgme trcygjeq zne acrreaz fhznefhzgahl hmqper- Gm
trhazgae, pnhz pe hre jcgm` gq hjjgm`, cyer hll jhzh tcgmzq, zne jgiieremae bezpeem cur
iumazgcm hmj zne w&yhlue ci zne jhzh tcgmz, qxuhrej?
g~
ggwhb~
2
Zngq gq zne jgqzhmae znhz pe hre fgmgfgqgm`-
Acmqgjer zne icllcpgm` qg~ jhzh tcgmzq?
Pnhz gq zne beqz igz lgme icr zngq jhzh3
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
6/23
Pell, acmqgjer zne znree tcqqgble lgmeq qncpm?
Gm zne ahqe ci zne blue lgme, znere gq mc lcqq icr zne znree tcgmzq znhz gz thqqeq znrcu`n,
buz h ihgrlw qubqzhmzghl lcqq icr zne czner znree tcgmzq?
Gi zne jgqzhmae hlcm` zne w&h~gq bezpeem zne blue lgme hmj zne jhzh tcgmzq gq a, znem zne
errcr, e, icr zne blue lgme gq?
21 ae
qgmae znere hre znree tcgmzq, hmj pe hre uqgm` zne xuhjrhzga jgqzhmae-
Qgfglhrlw icr zne rej lgme, gz quiierq mc lcqq icr zne znree tcgmzq znhz gz thqqeq znrcu`n,
buz h ihgrlw qubqzhmzghl lcqq icr zne czner znree tcgmzq, hmj zne errcr, e , icr zne rej lgme
gq hlqc?
21 ae
Gm zne ahqe ci zne `reem lgme znere hre errcrq icr hll qg~ tcgmzq, buz zne errcr gq cmlw nhlihq bg` gm ehan ahqe?
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Mcp, zne errcr gq?
22
2
2
1
:
9
29 aa
ae
Zngq fehmq znhz zne zczhl xuhjrhzga errcr icr zne `reem lgme gq nhli hq bg` hq gz gq icr
egzner zne blue cr zne rej lgmeq- Zngq gq beahuqe, pnem pe uqe zne xuhjrhzga, lhr`er
errcrq acumz fuan, fuan fcre znhm qfhller errcrq- Alehrlw, gm zngq ahqe, zne `reem lgme
pculj be zne beqz igz icr zneqe jhzh tcgmzq-
Me`hzgye cr Tcqgzgye Xug
Pgll zne thrhfezerq h hmj b be me`hzgye cr tcqgzgye icr zne jhzh qncpm belcp3
hb~w
Re`reqqgcm Icrfulh
Zne iumazgcm gq zne Nclw @rhgl ci lgmehr re`reqqgcm, hmj fuan ci qzhzgqzgaq gq
acmaermej pgzn ncp zc uqe zne jhzh zc jezerfgme zne yhlue ci b, hmj zne yhlue ci h- Gi
pe ahm jc zngq pgzn zne jhzh, znem pe nhye qclyej zne trcblef ci igzzgm` zne beqz lgme-
hb~w
Gi zne jhzh acfeq gm thgrq?
~8 ~2 ~1 ~M
w8 w2 w1 wM
Znem pe ahm ahlaulhze b uqgm` zne icrfulh?
g
g
g
gg
~~
ww~~
b2
Mcze znhz g^fehm~ hmj gWfehmw -
Treygcuqlw, peye uqej icr zne fehm, buz mcp znhz pe nhye fcre znhm cme yhrghblepe hre `cgm` zc uqe zne bhr&mczhzgcm-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Zngq icrfulh qnculjmz be emzgrelw umihfglghr- Pnem pe ahlaulhzej zne yhrghmae, pe
uqej? 2~~g , pnerehq mcp pe nhye 2&jgfemqgcmhl jhzh pe hre uqgm` ww~~ gg -
Mcp znhz pe kmcp b, hmj pe kmcp znhz?
hb~w
Gz zurmq cuz znhz zngq iumazgcm gq hlqc zrue icr zne hyerh`e yhlueq, ~ hmj w - Pe ahm
ahlaulhze zne yhlue icr h uqgm`?
~bwh
Lezq zrw gz cuz gm hm e~hftle-
Quttcqe pe nhye zne icllcpgm` jhzh qhftle?
~ w
9 0
2 1
8 2
&8 4
Mcp, pgzn zngq jhzh qez pe mczgae znhz zne w&yhlue gq hlphwq e~hazlw 8 lhr`er znhm zne
~&yhlue, qc?
8 ~w
Zngq fehmq znhz b 6 8 hmj h 6 8-
Lezq qee pnhz pe `ez pnem pe uqe zne icrfulh- Zne igrqz zngm` pe jc gq zc ahlaulhze
zne fehmq?
2:
>
:
8829
~
1:
82:
4210 w
Mcp pe ahm eyhluhze b uqgm`?
2222 28282229
1428122811221029
b
878489
78489
b
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Mcp pe ahm ahlaulhze h uqgm`?
8281 ~bwh
Pngan h`reeq pgzn cur gmgzghl cbqeryhzgcm-
Re`reqqgcm Xug
Ahlaulhze zne yhlueq icr h hmj b icr zne icllcpgm` jhzh qez?
~ w
: 0
1 7
0 82 88
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Acrrelhzgcm
Zngq qeazgcm gq hll hbcuz acrrelhzgcm- Acrrelhzgcm gq h fehqure ci ncp alcqelw zpc
yhrghbleq hre relhzej- Pe ahm ahlaulhze qcfezngm` ahllej zne acrrelhzgcm aceiigagemz
pngan `gyeq uq h fehqure ci ncp alcqelw zpc yhrghbleq hre relhzej-
Zne acrrelhzgcm aceiigagemz, r, pgll nhye h yhlue bezpeem &8 hmj 8, qc znhz?
88 r
Gi zne jhzh gq acftlezelw lgmehr, pgzncuz mcgqe, hq qncpm belcp, znem pe ahm igz h lgme
e~hazlw zc zne jhzh hmj zne acrrelhzgcm pgll be 8?
Gi zne jhzh gq acftlezelw umrelhzej znem zne acrrelhzgcm pgll be 4?
Zne acrrelhzgcm aceiigagemz ahm hlqc be &8 gm zne ahqe pnere zne jhzh gq qzgll terieazlw
hlg`mej zc zne lgme, buz pnere znere gq h me`hzgye relhzgcmqngt bezpeem zne zpc
yhrghbleq hq qncpm?
http://en.wikipedia.org/wiki/Correlation_and_dependencehttp://en.wikipedia.org/wiki/Correlation_and_dependence -
7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
11/23
Acrrelhzgcm Ircf Re`reqqgcm Xug
Quttcqe znhz pe rhm lgmehr re`reqqgcm cm cur jhzh, hmj pe icumj znhz?
b 6 :
h 6 &1
Pnere zneqe yhlueq jeqargbe zngq lgmehr relhzgcmqngt bezpeem ~ hmj w?
w 6 :~ 1
Pngan ci zne icllcpgm` qzhzefemzq hbcuz zne acrrelhzgcm aceiigagemz, r, gq zrue3
r gq tcqgzgye r gq me`hzgye r 6 4 Pe ahmz zell
Acrrelhzgcm Icrfulh
Qc, zc quffhrgqe pnhz pe kmcp qc ihr hbcuz zne acrrelhzgcm aceiigagemz?
Gz nhq h yhlue bezpeem &8 hmj 8 Gz zellq uq ncp relhzej zpc yhrghble hre Bczn +8 hmj &8 jeqargbe terieazlw lgmehr jhzh
Qc ncp jc pe acftuze h yhlue icr r3
Pell, cme phw zc acftuze zne acrrelhzgcm aceiigagemz gq yerw qgfglhr zc zne phw znhz
pe ahlaulhzej zne yhlue ci b pnem pe lcckej hz lgmehr re`reqqgcm?
g g
gg
g
gg
ww~~
ww~~
r22
Pnere? g~M
~8
hmj gwM
w8
Mcp zngq gq trcbhblw zne fcqz acftle~ icrfulh znhz wcu nhye emacumzerej qc ihr gm
zngq alhqq, buz wcu pgll qee gz gq relhzej zc h lcz ci zne qzuii pe nhye qeem beicre, lgke
yhrghmae hmj qc cm, hmj znhz uqgm` gz gq mcz znhz jgiigaulz gm trhazgae-
-
7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Gi pe lcck hz zne jemcfgmhzcr?
g g
gg ww~~22
Pe mczgae znhz zne zerf pgzngm zne qxuhre rccz gq zne trcjuaz ci zne mcm&mcrfhlgqej
yhrghmae ci ~ hmj zne mcm&mcrfhlgqej yhrghmae ci w-
Zne muferhzcr gq h kgmj ci fg~ej&yhrghmae?
g
ggww~~
Zngq gq qcfezgfeq ahllej zne acyhrghmae, beahuqe gz ahlaulhzeq zne yhrghmae cyer zpc
ac&caaurrgm` yhrghbleq- Ncpeyer, wcu pgll nhye mczgaej znhz, cmae h`hgm, znere gq h
fgqqgm` mcrfhlgqer- Pnhz nhq nhttemej gq znhz zne mcrfhlgqerq cm zne muferhzcr hmjjemcfgmhzcr ahmael ehan czner cuz-
Acftuzgm` Acrrelhzgcm
Lezq zrw zne icrfulh cuz cm qcfe jhzh-
~? 1 : 5
w? 0 > 7
Gz gq ehqw zc qee znhz zne fehm ci ~ gq?
:1
825:1
1
8~
hmj zne fehm ci w gq?
>1
2:7>0
1
8w
Hrfej pgzn zneqe fehm yhlueq pe ahm ahlaulhze zne icllcpgm`?
~~ &8 4 8
ww &8 4 8
Pe ahm tlu` zneqe yhlueq gmzc cur exuhzgcm, hmj pe `ez?
8
22
2
848848
884488
222222
r
-
7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Lezq lcck hz h jgiieremz jhzhqez,?
~? 1 : 5
w? 2 5 >
H`hgm, pe ahlaulhze zne fehmq?
:1
825:1
1
8~
51
85>52
1
8w
@ueqq r Xug
Beicre pe jc zne ahlaulhzgcm, lezq qee pnhz wcur gmzugzgcm qhwq hbcuz zne yhlue icr r gm
zngq ahqe- Pngan ci zne icllcpgm` jc wcu zngmk gq acrreaz3
r 6 8 r 6 1 r 6 2 r 6 4
Mcp lezq zhbulhze zne jgiieremaeq ircf zne fehmq?
~~ &8 4 8
ww &1 4 1
H`hgm, pe ahm tlu` zne yhlueq gmzc cur icrfulh zc `ez?
8
8>2
9
141848
184418
222222
r
Pngan gq hq pe e~teazej-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Reyerqe Crjer
Lezq qee pnhz nhttemq gi pe anhm`e zne crjer ci zne w&yhlueq hq qncpm?
~? 1 : 5
w? > 5 2
Qgmae cmlw zne crjer nhq beem anhm`ej hmj zne hazuhl yhlueq hre umanhm`ej, zne fehm
yhlueq pgll be zne qhfe hq beicre?
:1
825:1
1
8~
51
8525>
1
8w
Mcp, qgmae zne w&yhlueq jearehqe hq zne ~&yhlueq gmarehqe pe pculj e~teaz zne
acrrelhzgcm aceiigagemz zc be me`hzgye- Lezq qee pnhz nhttemq pnem pe ahlaulhze zne
yhlue ci r-
Zhbulhzgm` zne jgiieremaeq ircf zne fehmq `gyeq?
~~ &8 4 8
ww 1 4 &1
Hmj cmae h`hgm, pe ouqz tlu` zne yhlueq gmzc cur icrfulh?
8
8>2
9
141848
184418
222222
r
Qc zne jhzh gq terieazlw me`hzgyelw acrrelhzej-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Umacrrelhzej Jhzh
Lezq zrw qcfezngm` h lgzzle bgz zrgakw- Lezq anhm`e zne w&yhlueq zc?
~? 1 : 5
w? > 5 >
Pnhz qeefq zc be nhttemgm` gq znhz zne w&yhlueq qzhrz zc jearehqe hq zne ~&yhlueq
gmarehqe, buz znem znew qzhrz zc gmarehqe h`hgm- Pngle znere fhw be h relhzgcmqngt
bezpeem ~ hmj w, gz jceqmz httehr zc be h lgmehr cme, hmj pe pculj e~teaz zne
acrrelhzgcm zc be erc-
Lezq jc zne ahlaulhzgcm- Zne fehmq hre mcp?
:
1
825:1
1
8~
01
28>5>
1
8w
Mcp pnem pe zhbulhze zne jgiieremaeq ircf zne fehmq pe `ez?
~~ &8 4 8
ww 8 &2 8
Hmj gi pe tlu` zne yhlueq gmzc cur icrfulh pe `ez zne acrrelhzgcm aceiigagemz?
4
92
4
828848
882488
222222
r
Ci acurqe, pe jgjmz hazuhllw meej zc ahlaulhze zne jemcfgmhzcr- Cmae pe kmep zne
muferhzcr phq erc pe hlqc kmep znhz r 6 4-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Igmhl E~hftle
Lezq lcck hz h igmhl e~hftle- Zngq gq cur jhzh?
~? 1 : 5
w? > 1 0
Alehrlw, zngq jceqmz lcck yerw acrrelhzej, hlzncu`n gz lcckq fcre acrrelhzej znhm zne
jhzh gm zne lhqz e~hftle qgmae zne igmhl w&yhlue nhqmz gmarehqej bw hq fuan- Pe fg`nz
znereicre e~teaz znhz zne acrrelhzgcm aceiigagemz pgll be leqq znhm 8, hmj gi pe tlcz zne
jhzh cm h `rhtn, pe qee znhz gz qnculj hlqc be me`hzgye?
Hq uquhl, zne igrqz zngm` pe jc gq zc ahlaulhze zne fehm yhlueq icr ~ hmj w?
:1
825:1
1
8~
91
8>01>1
8 w
Mcp pnem pe zhbulhze zne jgiieremaeq ircf zne fehmq pe `ez?
~~ &8 4 8
ww 2 &1 8
Hmj gi pe tlu` zne yhlueq gmzc cur icrfulh pe `ez zne acrrelhzgcm aceiigagemz?
8>7-48:2
8
812848
881428222222
r
Qc znere gq h me`hzgye acrrelhzgcm, hq pe quqteazej, buz gz gq pehk- Zngq jhzh rehllw
gqmz pell jeqargbej bw h lgmehr iumazgcm-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Quffhrw
Wcu mcp umjerqzhmj zne bhqgaq ci acrrelhzgcm aceiigagemzq- Hq pe qhgj ehrlger, zne
acrrelhzgcm aceiigagemz?
nhq h yhlue bezpeem &8 hmj 8 zellq uq ncp relhzej zpc yhrghble hre
Pe hlqc mcp kmcp znhz?
Gi r = 4 znere gq h tcqgzgye relhzgcmqngt bezpeem ~ hmj w- Gi r < 4 znere gq h me`hzgye relhzgcmqngt bezpeem ~ hmj w- Gi r 6 4 znere gq mc relhzgcmqngt bezpeem ~ hmj w-
Iurznerfcre, pe nhye qeem znhz 8r hq zne relhzgcmqngt bezpeem ~ hmj w beacfeq
gmarehqgm`lw lgmehr- Bczn r 6 +8 hmj r 6 8 jeqargbe terieazlw lgmehr jhzh pgzncuz hmwmcgqe cr jeyghzgcm ircf zne lgme-
Acrrelhzgcm gq h yerw tcperiul zccl- Icr hmw jhzh qez pgzn fulzgtle yhrghbleq, quan hq
qhlhrw yerquq h`e, wcu ahm mcp zell ncp alcqelw zne yhrghbleq relhze zc ehan czner
uqgm` zne relhzgyelw qgftle icrfulh?
g g
gg
g
gg
ww~~
ww~~
r22
-
7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
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Fcmzw Nhll Trcblef .Ctzgcmhl'
Zngq qeazgcm qnculj be ium- Gz gq, ncpeyer, emzgrelw ctzgcmhl-
Qcfe ci wcu fhw be ihfglghr
pgzn Fcmzw Nhll- Ne rhm h UQ`hfe qncp ahllej Lezq Fhke h
Jehl ircf 8791- Zne qncp rhm
icr fhmw wehrq-
Hz zne nehrz ci zne `hfe qncp
phq h tule- Zngq tule tuleq
qzhzgqzgaghmq zc zne treqemz jhw- Gm
zngq umgz, wcu `ez zne anhmae zc
qclye zne Fcmzw Nhll trc`rhf,
hmj wcu hlqc `ez zne anhmae zc
trc`rhf gz, hmj yergiw znhz zne
hqqerzgcm pngan gm mcz emzgrelw
cbygcuq gq hazuhllw acrreaz-
Gm zne `hfe znere hre znree jccrq- Bengmj cme jccr gq h ahr- Fcmzw kmcpq pngan jccr,
buz ne pcmz zell wcu pnere zne ahr gq-
Zne `hfe gq znem tlhwej hq icllcpq?
Wcu `ez zc anccqe h jccr- Qhw, icr zne qhke ci hr`ufemz znhz wcu tgak jccr mufber 2-
Gi zne ahr gq bengmj jccr 2, znem wcu pgm zne ahr, cznerpgqe wcu pgm mczngm`- Qc ihr, qc
`ccj-
Mcp acfeq zne gmzereqzgm` bgz- Cbygcuqlw, hz lehqz cme ci zne zpc refhgmgm` jccrq
jceqmz nhye h ahr bengmj gz- Mcp, Fcmzw kmcpq pngan jccr nhq zne ahr, hmj nereyehlq cme ci zne jccrq znhz wcu jgjmz anccqe znhz jceqmz nhye zne ahr-
Fcmzw znem hqkq wcu gi wcu phmz zc qpgzan ircf zne jccr wcu nhye ancqem zc zne czner
alcqej jccr- Jc wcu phmz zc anhm`e wcur ancgae gm zne ncte znhz wcu pgll gmarehqe
wcur anhmae ci pgmmgm` zne ahr3
Pnhz fhkeq zngq trcblef gmzereqzgm` gq znhz pnem Fcmzw ctemej zne jccr, ne rehllw
jgjmz zell wcu hmwzngm` wcu jgjmz hlrehjw kmcp- Wcu hlrehjw kmep gm hjyhmae znhz
cme ci zne zpc jccrq jgjmz acmzhgm zne ahr- Zne ihaz znhz Fcmzw nhq ouqz ctemej h
jccr qnculj `gye wcu erc gmicrfhzgcm hbcuz pngan ci zne refhgmgm` jccrq zne ahr gq
bengmj-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
19/23
Gi wcu ancqe jccr 2, hmj Fcmzw znem ctemej jccr 1, hll wcu mcp kmcp gq znhz jccr 1
jceqmz acmzhgm zne ahr- Pnw qnculj jccr 8 mcp be fcre lgkelw znhm jccr 23
Jccr Anhmae Xug
@gyem znhz wcu ancqe jccr 2, hmj Fcmzw znem reyehlej znhz jccr 1 jgjmz acmzhgm zne
ahr, pnhz hre zne trcbhbglgzgeq, T8, T2 hmj T1 znhz zne ahr gq bengmj ehan jccr3
Ci acurqe gz gq ehqw zc qee znhz T1 6 4- Pe hlrehjw kmep znhz zne ahr phqmz bengmj
jccr 1-, Buz jcmz pcrrw gi wcu peremz hble zc ig`ure cuz zne czner zpc trcbhbglgzgeq,
zne hmqper zc zngq trcblef gq emzgrelw mcm&gmzugzgye-
Pe ahm ternhtq beqz umjerqzhmj pnhz gq nhttemgm` bw bugljgm` h zruzn zhble-
Znere hre znree tcqqgble zrue lcahzgcmq icr zne ahr, hmj pe kmcp znhz ehan ci zneqe
tcqqgble lcahzgcmq nhq h trcbhbglgzw ci 8#1-
Pnem pe anccqe h jccr, Fcmzw pgll ctem cme ci zne czner jccrq- Pe ahm acmqzruaz
zne zruzn zhble hq qncpm?
Zrue
lcahzgcm
Fcmzw
Nhll Trcbhbglgzw
Mcrfhlgqej
trcbhbglgzw
8 8 4
8 2 4T.8' 6 8#1
8 1 8#1
2 8 8#9
2 2 4T.2' 6 8#12 1 8#9
1 8 8#1
1 2 4T.1' 6 8#1
1 1 4
Lezq qhw, icr zne qhke ci hr`ufemz znhz pe nhye ancqem jccr mufber 2- Mcp, pe
kmcp znhz cm zne igrqz rcp ci zne zruzn zhble, gi zne ahr gq bengmj jccr mufber 8 znem
zne trcbhbglgzw znhz Fcmzw pgll ctem jccr mufber 8 gq erc- Cm zne qeacmj lgme, zne
trcbhbglgzw znhz Fcmzw pgll ctem jccr 2 gq hlqc erc beahuqe pe nhye ancqem jccr
mufber 2-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
20/23
Qc zne cmlw ctzgcm refhgmgm` gq icr Fcmzw zc ctem jccr 1- Zngq nhq h trcbhbglgzw ci 8,
buz zne tcqzergcr trcbhbglgzw fuqz zhke haacumz znhz zne zczhl trcbhbglgzw icr T.8' 6 1,
qc zne trcbhbglgzw beacfeq 1#81#88 -
Qgfglhrlw icr zne ahqe pnere zne ahr gq bengmj jccr mufber 1, zne trcbhbglgzw znhz
Fcmzw pgll ctem jccr mufber 1 gq erc, hq gq zne trcbhbglgzw znhz ne pgll ctem zne jccrznhz pe nhye ancqem .jccr mufber 2'- Zne cmlw refhgmgm` ancgae gq jccr mufber 8-
Gi zne ahr gq bengmj jccr mufber 2, hmj pe nhye ancqem jccr mufber 2 znem znere gq h
igizw anhmae icr jccr mufber 8 cr jccr mufber 1- Zne tcqzergcr trcbhbglgzw icr bczn
jccrq gq znereicre -9#81#82#8
Mcp pe nhye cur zruzn zhble bhqej cm zne ihaz znhz pe ancqe jccr mufber 2-
Lezq qhw znhz Fcmzw ctemq jccr mufber 1- Mcp eyerw czner ahqe, gm pngan ne fg`nz
nhye tgakej jccr mufber 8 cr jccr mufber 2 nhq erc trcbhbglgzw- Zne cmlw eyemzq
znhz refhgm hre ng`nlg`nzej nere?
Zrue
lcahzgcm
Fcmzw
Nhll Trcbhbglgzw
Mcrfhlgqej
trcbhbglgzw
8 8 4
8 2 4T.8' 6 8#1
8 1 8#1 2#1
2 8 8#9
2 2 4T.2' 6 8#12 1 8#9 8#1
1 8 8#1
1 2 4T.1' 6 8#1
1 1 4 4
Mcp pe ouqz meej zc mcrfhlgqe zneqe yhlueq qc znhz zne zczhl trcbhbglgzw hjjq ut zc 8-
Aurremzlw zne quf ci zne trcbhbglgzgeq gq 2#89#81#8 - Gi pe jgygje ehan gmjgygjuhltrcbhbglgzw bw zngq quf pe `ez zne mcrfhlgqej trcbhbglgzgeq hq qncpm- Zneqe hre zne
zrue tcqzergcr trcbhbglgzgeq `gyem znhz pe ancqe jccr mufber 2, hmj Fcmzw ctemej
jccr mufber 1-
Alehrlw pe qnculj qpgzan cur ancgae eyerw zgfe, hq zngq pgll jcuble cur anhmaeq ci
pgmmgm` zne ahr(
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
21/23
Qgfulhzgcm
Prgze h iumazgcm qgfulhze.' znhz rumq 8444 gzerhzgcmq ci h qgfulhzgcm ci zne Fcmzw Nhll
trcblef hmj qc eftgrgahllw yergiw zne trcbhbglgzgeq znhz pe nhye ouqz ahlaulhzej-
Zne iumazgcm qnculj acumz ncp fhmw zgfeq wcu pgm zne ahr gm h yhrghble, K, hmj znemrezurm K jgygjej bw zne mufber ci gzerhzgcmq, M-
Twzncm gmalujeq zne buglz&gm iumazgcm rhmjgmz.'- Zngq `emerhzeq rhmjcf gmze`erq gm zne
rhm`e qteagigej bw zne iumazgcm hr`ufemzq, qc?
rhmjgmz.8,1'
pgzn rezurm h rhmjcf gmze`er gm zne rhm`e 8 zc 1 .pngan gq e~hazlw pnhz wcu pgll meej
gm crjer zc tgak h rhmjcf jccr'-
Wcu pgll hlqc nhye zc qgfulhze zne hazgcmq ci Fcmzw Nhll- Qcfezgfeq zneqe hazgcmq
pgll be jezerfgmgqzga, hz czner zgfeq znew pgll be qzcanhqzga .rhmjcf'- Reahll znhz pe
qhp bczn zwteq ci hazgcm pnem pe acmqzruazej zne zruzn&zhble-
Cmae zne Fcmzw&qgfulhzcr nhq tgakej h jccr, ilgt wcur ancgae zc zne refhgmgm` jccr-
Gi znhz fhzaneq zne zrue lcahzgcm znem wcu qnculj gmarefemz K, cznerpgqe mcz-
Pnem wcu rum zngq 8444 zgfeq, zne cuztuz ircf wcur iumazgcm qnculj be httrc~gfhzelw
exuhl zc 2#1-
Zne hqqg`mfemz pgll rexugre qcfe rehl kmcplej`e ci Twzncm hmj gq znereicreacmqgjerej zc be h anhllem`gm` trcblef- @ccj luak-
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
22/23
Hmqperq
Tgak zne Lgme Xug
a
Igmj Aceiigagemzq Xug
h 6 8
b 6 4-25
Me`hzgye cr Tcqgzgye Xug
h gq tcqgzgye- Hq ~ gmarehqeq, w jearehqeq, qc b gq me`hzgye- Zngq gq hm e~hftle
cime`hzgye acrrelhzgcm-
Re`reqqgcm Xug
:~
0w
28:
2>b
h 6 85
Acrrelhzgcm Ircf Re`reqqgcm Xug
r gq tcqgzgye r gq me`hzgye r 6 4 Pe ahmz zell
@ueqq r Xug
r 6 8
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7/31/2019 Course Notes for Unit 6 of the Udacity Course ST101 Introduction to Statistics
23/23
Jccr Anhmae Xug
T8 6 4-990
T2 6 4-111
T1 6 4
Qgfulhzgcm
ircf rhmjcf gftcrz rhmjgmz
M 6 8444
jei qgfulhze.M'?
K 6 4icr g gm rhm`e.M'?ZrueLca 6 rhmjgmz.8,1'`ueqq 6 rhmjgmz.8,1'gi ZrueLca 66 `ueqq?
fcmzw 6 rhmjgmz.8,1'
pngle fcmzw 66 ZrueLca?fcmzw 6 rhmjgmz.8,1'
elqe?fcmzw 6 9 & ZrueLca & `ueqqqpgzan 6 9 & `ueqq & fcmzwgi qpgzan 66 ZrueLca?
K 6 K + 8
rezurm ilchz.K' # ilchz.M'
trgmz qgfulhze.M'
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