probability-and-distribution.pdf

7/30/2019 Probability-and-Distribution.pdf

1/21


2/21

5

Ecaptjr 7 Latcjlatdes

YCJ KAYJ AEAIJLT _PY"FYI" C"M"> %;9& Hjscava Hrupa #tcdri @fmmr$& 5?tc

Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11

> ?3?,0:;??;:?& db`mOtcjkatjaeaijly"eml Empyrdkct rjsjrvji" [jg> www"tcjkatjaeaijly"eml _akj 53

ECA_YJW 7_rmgagdfdty abi Idstrdgutdmb

1" _jrlutatdmbDt ds tcj arrabkjljbt m` tcj kdvjb tcdbks #mgnjets$ db smlj ij`dbdtj mrijr"Easjsa$ Id``jrjbt tcdbks> Bm" m` pjrlutatdmbs m` b id``jrjbt tcdbks tahjb aff at a tdlj < b!

JxalpfjBm" m` pjrlutatdmb m` wmri KAYJ < 9!g$ Efassjs m` jquaf tcdbks> Bm" m` pjrlutatdmbs m` b mgnjets m` wcdec arj afdhj arjafdhj abi arj afdhj < !!!!e$ Ycj bulgjr m` id``jrjbt pjrlutatdmbs m` b id``jrjbt tcdbks tahjb r at a tdlj

wdtcmut rjpjtdtdmb < b_r

!

i$ Ycj bulgjr m` id``jrjbt pjrlutatdmbs m` b id``jrjbt tcdbks tahjb r at a tdlj wdtc

rjpjtdtdmb < JxalpfjDb a emiji tjfjkral tcj fjttjrs a g e arj arrabkji db krmup m` twm fjttjrs eaffji wmris" Cmwlaby id``jrjbt suec wmris eab gj emiji=

UmfutdmbKdvjb 5 fjttjrs arj a g e" Ujfjet 7 wdtc rjpjtdtdmbs 5 < 4 #ag ga ae ea ge eg aa gg ee$

Db tcds prmgfjl bulgjr m` id``jrjbt suec wmris embtadbdbk jaec fjttjr bm lmrj tcabmbej#wdtcmut rjpjtdtdmb$ ds 5_7 70:


3/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


A G

7" Emlgdbatdmb

Bulgjr m` emlgdbatdmbs m` b id``jrjbt mgnjets tahjb r at a tdlj wdtcmut rjpjtdtdmbsds bEr


4/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11

> ?3?,0:;??;:?& db`mOtcjkatjaeaijly"eml Empyrdkct rjsjrvji" [jg> www"tcjkatjaeaijly"eml _akj 9?

0" Jquaffy fdhjfy jvjbtsD` mbj m` tcj jvjbts eabbmt cappjb db prj`jrjbej tm mtcjr tcjb suec jvjbts arj sadi tm gj

jquaffy fdhjfy"

BmtjYcrmwdbk a idj #afsm turbdbk up m` tcj sdx id``jrjbt `aejs m` tcj idj$ ds jxcaustdvj lutuaffyjxefusdvj abi jquaffy fdhjfy jvjbts"

Miis db `avmur m` ab jvjbt


5/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


11" Ycjmrjl m` emlgdbji prmgagdfdtyD` tcj prmgagdfdty m` ab jvjbt A cappjbdbk as a rjsuft m` trdaf ds _#A$" _rmgagdfdty m` ab

jvjbt G cappjbdbk as a rjsuft m` trdaf a`tjr A cas cappjbji ds _#G-A$ tcjb tcj prmgagdfdtym` gmtc tcj jvjbts A abi G cappjbdbk ds

_ #AG$< _#A$" _#G-A$ X _#A$?\< _ #G$" _#A-G$ X _#G$?\

Ycds ds afsm hbmwb as luftdpfdeatdmb tcjmrjl"@mr dbijpjbijbt jvjbts A&G _#G-A$ < _#G$ _#A-G $< _#A$Cjbej _#AG$ < _#A$ _#G$

Dlpmrtabt pmdbtD` & arj prmgagdfdtdjs m` twm dbijpjbijbt jvjbts tcjb1" #1,$ prmgagdfdty m` `drst jvjbt cappjbs abi sjembi `adfs #d"j mbfy `drst cappjbs$7" #1,$#1, prmgagdfdty m` gmtc jvjbt `adfs5" 1,#1,$#1, prmgagdfdty m` at fjast mbj jvjbt meeur9" prmgagdfdty m` gmtc jvjbt meeurs17" Gayjs Ycjmrjl

Ab jvjbt A emrrjspmbis tm a bulgjr m` jxcaustdvj jvjbts "" "D` _# abi _#A-$ arj kdvjb tcjb

_ %;9& Hjscava Hrupa #tcdri @fmmr$& 5?tc

Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


_ #A-[$


7/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


_rmgagdfdty m` tcj ecmsjb trdabkfj tm gj jqudfatjraf


8/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


G ; # 59 $ # 9 5 $# 7 : $ # : 7 $ # 1 0 $ # 0 1 $ < _ #A$ < _#$ < _#G$ < _# $ < _ #A$ `mr wdbbdbk %;9& Hjscava Hrupa #tcdri @fmmr$& 5?tc

Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11

> ?3?,0:;??;:?& db`mOtcjkatjaeaijly"eml Empyrdkct rjsjrvji" [jg> www"tcjkatjaeaijly"eml _akj 9:

Embtdbumus rabiml vardagfjD` a rabiml vardagfj tahjs db`dbdtj bulgjr m` ubemubtagfj vafujs dt ds eaffji a embtdbumusrabiml vardagfj"

Ldxji rabiml vardagfjDb tcds smlj vafujs lay gj idserjtj abi smlj vafujs lay gj embtdbumus"

Aff tcj rabiml vardagfjs arj ijserdgji gy>

_rmgagdfdty Ijbsdty @ubetdmb #Idserjtj pi`$ Eulufatdvj Idstrdgutdmb @ubetdmb #ei`$1:" Idserjtj _rmgagdfdty Ijbsdty @ubetdmb #pi`$ mr _rmgagdfdty Lass @ubetdmb

Ycj sjt m` vafujs Sd wdtc tcjdr prmgagdfdtdjs embstdtutj a prmgagdfdty idstrdgutdmb mrprmgagdfdty ijbsdty `ubetdmb m` tcj idserjtj vardagfj S" D` `#x$ ds tcj pi` tcjb `#


10/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


13" Embtdbumus Eulufatdvj Idstrdgutdmb `ubetdmb #ei`$mr Idstrdgutdmb @ubetdmbD` < _#Sx$


11/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11

> ?3?,0:;??;:?& db`mOtcjkatjaeaijly"eml Empyrdkct rjsjrvji" [jg> www"tcjkatjaeaijly"eml _akj 9;

< h ( 5h(:h(;h %;9& Hjscava Hrupa #tcdri @fmmr$& 5?tc

Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


a" _X x a \ < _X x a \g" _ X x 2 g \ < ?"?:Umfutdmba" <

5 < 5 5 < 1,5 7 5


13/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


9" Par#x,h$ < Par#x$ ,Xh ds embstabt\

:" Par#ax(gy$ < Par#x$ ( Par#y$ 7ag emv#xy$ #d` bmt dbijpjbijbt$XA & G arj embstabts\

< Par#x$ ( Par#y$ #d` dbijpjbijbt$71" Emvardabej

Emv #xy$


14/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11

> ?3?,0:;??;:?& db`mOtcjkatjaeaijly"eml Empyrdkct rjsjrvji" [jg> www"tcjkatjaeaijly"eml _akj :?

_rmgagdfdty m` H sueejss ds _ #$ Ljab < vardabej


15/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11

> ?3?,0:;??;:?& db`mOtcjkatjaeaijly"eml Empyrdkct rjsjrvji" [jg> www"tcjkatjaeaijly"eml _akj :1

5" As x dberjasjs buljrdeaffy `#x$ ijerjasjs rapdify"9" Ycj laxdlul prmgagdfdty meeurs at tcj pmdbt

< abi kdvjb gy

%;9& Hjscava Hrupa #tcdri @fmmr$& 5?tc

Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


< : (


17/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


#d$ _#1 ij`jetdvj$ <

#dd$ _#bmbj ij`jetdvj$ <

#dd$ _#at lmst 7 ij`jetdvj$


18/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


Umfutdmbz7


19/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11

> ?3?,0:;??;:?& db`mOtcjkatjaeaijly"eml Empyrdkct rjsjrvji" [jg> www"tcjkatjaeaijly"eml _akj ::

Dlpmrtabt pmdbts Ljab ds gjst ljasurjljbt # aff mgsjrvatdmbs tahjb$" Lmij ds wmrst ljasurjljbt # mbfy laxdlul `rjqujbey ds tahjb$" Db ljidab :? * mgsjrvatdmb ds tahjb" Uul m` tcj ijrdvatdmb agmut ljab ds zjrm" Uul m` tcj agsmfutj ijrdvatdmbs agmut ljidab ds ldbdlul" Uul m` tcj squarj m` tcj ijrdvatdmbs agmutljab ds ldbdlul"

73" Em,j``dedjbt m` vardatdmbWatdm m` U"I" abi ljab ds eaffji as em,j``dedjbt m` vardatdmb"

Emj``dedjbt m` vardatdmb


20/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11


_rmpjrtdjs m` Nmdbt idstrdgutdmb ùbetdmb- eullufatdvj idstrdgutdmb ùbetdmb>1"

@ < ?

7" @ < 15" @ < ? { @ < _S T y < ? x 1 < ? }9" @x < _S x T < @x " 1 < @x:" @ y < @y57" Nmdbt prmgagdfdty ijbsdty ùbetdmb

Ij`dbji as `x y < @x y_rmpjrty> `x y ix iy

< 1

Bmtj> S abi T arj sadi tm gj dbijpjbijbt rabiml vardagfj

D` `xy#xy$ < `x#x$ " `T#y$

Jxalpfj@mr a krmup m` 1?? eabidiatjs ljab


21/21

5



Ermss& 1?tc

Ladb& Nayabakar 9tc

Gfmeh& Gabkafmrj,11

< :? 7 Pardabej

probability-and-distribution.pdf

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