8/10/2019 Lecture1-2407.pdf

1/27

!"#$%& ( ")*+),,-+)* .)/ 0)1,-2.+)23

4).536+6 7.-2 #7-89.9+5+23 .)/ :2.;6;16

.68) ?5.@, !8A,)"(B.+5C 1,,1D9E)F6=,/F=6*

GH1,C "I4(%J(%$

GK,) GH1, L8F-6C MAF-6/.3 I%(II.B

8/10/2019 Lecture1-2407.pdf

2/27

!5.66 N8*+6;16C!"#$%&'()"* ,#'&-"# ,#./0N+ OF+B+) P"Q"R1-(#'$-,0

o

75,.6, 18B, 8) ;B, .)/ /8 )82 5,.S, ,.-53= T2 +6 +BK8-2.)2 28 .U,)/ .55 5,12F-,6Vo

8/10/2019 Lecture1-2407.pdf

3/27

M8K+16 W8- 2A, O,B.+)/,- 8_ 2A, !5.66C$%:.:)3)#5 #7-%$5O.)/8B ,S,)26 .)/ /,g)+;8) 8_ K-89.9+5+23h 18)/+;8).5 K-89.9+5+23h 2A,8-,B 8_ 282.5

K-89.9+5+23 .)/ ?.3,6i 2A,8-,Bh 62.;6;1.553 +)/,K,)/,)2 ,S,)26hC$%:.:)3)#5 &),#$):'A%",

8/10/2019 Lecture1-2407.pdf

4/27

TjMOG

8/10/2019 Lecture1-2407.pdf

5/27

:8B, 8_ 2A, B.)3 /+m,-,)2 23K,6 8_ F)1,-2.+)23 Z, _.1, +)15F/,CI= N.1@ 8_ f)8Z5,/*, ` a8/,5 +BK,-_,1;8) P,K+62,B+1 F)1,-2.+)23R

#= T)A,-,)2 KA36+1.5X 1A,B+1.5X 9+858*+1.5X .)/ 82A,- ).2F-.5S.-+.9+5+23 P.5,.28-3 F)1,-2.+)23R

d=

T)18BK5,2, +)_8-B.;8) ` F)/,-(6.BK5,/ +)_8-B.;8) 6K.1,P62.;6;1.5 F)1,-2.+)23R

L8Z 9,62 28 2-,.2 S.-+8F6 ,)*+),,-+)* .)/ 2,1A)+1.5 K-895,B6.118F);)* _8- 2A, ,^+62,)1, 8_ 6F1A F)1,-2.+);,6o

4KK53 9.6+1 K-89.9+5+23 .)/ 62.;6;16 18)1,K26V

0)1,-2.+)23

8/10/2019 Lecture1-2407.pdf

6/27

0)1,-2.+)23 "^.BK5, p ZA.2 23K, +6 2A+6o:-($;&*< =/04 &. >*&,3(8+( ? @&8(3 #'A(1.(0;&*B

qN826 8_ )8+6,X 9F2r

s

:+\, 8_ )8+6, +6 6B.55,- 68B,;B,6 2A.) 2A, 1A.)*, +) 2A, 62.2,t4)/ 82A,- ;B,6 2A, )8+6, +6 5.-*,- 2A.) 2A, 1A.)*, +) 2A, 62.2,

8/10/2019 Lecture1-2407.pdf

7/27

0)1,-2.+)23 "^.BK5,C

4)6Z,-C C*"(1(*) A"D$#0/3E 0"('#0/3E 6#&3&+#0/3E/*8 &)"(1 */)-1/3 2/1#/6#3#)D4j< C*0&'A3()(#*.&1'/;&* ? -*8(15$/'A3(8 #*.&1'/;&* $A/0(

8/10/2019 Lecture1-2407.pdf

8/27

8/10/2019 Lecture1-2407.pdf

9/27

!8)2-85 ` :2.)/.-/6 F)/,-0)1,-2.+)23

O,*F5.28-3 98/3 ),,/6 28 6K,1+_3 68B, 18)2-85e62.)/.-/6 28 ,)6F-,1,-2.+) B+)+BFB 5,S,5 8_ [F.5+23eK,-_8-B.)1,

M88 62-+)*,)2 ( A+*A K-8/F1;8) 1862X ./A,-,)1, .)/ ,)_8-1,B,)2 1.)9, /+H1F52

M88 5.^ ( [F.5+23 8_ K-8/F12 18BK-8B+6,/

T_ 2A, 18)2-85 8- /,6+*) S.-+.95,6 .-, -.)/8BX ZA.2 +6 288 5.^ 8- 28862-+)*,)2o

411,K2.)1, 62.)/.-/6 8F*A2 28 9, /,S,58K,/ 8) 2A, 9.6+6 8_A1&6/6#3#)D 0&*$#8(1/;&*$

8/10/2019 Lecture1-2407.pdf

10/27

@-D$-,-"A"* G.#. 9)#7 . H),#%*$.4

MA, (7.$.(#-$),A(,8_ . 6,2 8_ /.2. 1.) 9, D%$#$.5-& *$.D7)(.335+) 2A,_8-B 8_ . 7),#%*$.4 8- I$-6'-"(5 &).*$.4=

MA,6, 1A.-.12,-+6;16 B.3 +)15F/, P.55 28 9, .//-,66,/ +) 2A+6 15.66RC a,.)

a8/, Q.-+.9+5+23 :@,Z),66

8/10/2019 Lecture1-2407.pdf

11/27

L8Z 28 !8)62-F12 . L+628*-.BI= !A886, . -.)*, 8) 2A, .961+66. P^(.^+6R 2A.2 +)15F/,6 2A, B.^+BFB `

B+)+BFB 896,-S,/ S.5F,6#= !A886, .) .KK-8K-+.2, 61.5+)* 8_ 2A, .961+66. P5+),.-X 58*.-+2AB+1X ,21=Rd=

8/10/2019 Lecture1-2407.pdf

12/27

L,-, +6 . ;'(5$(1#($8_ 2A, /.+53 .S,-.*, .+- K855F;8)

5,S,5 +) :+)*.K8-,= T2 588@6 5+@, +2 18)2.+)6 .18B9+).;8) 8_ $#+*/3$.)/ *$(= MA,-, +6 . 582 8_#*.&1'/;&*A,-,= N,2 F6 F6, . A+628*-.B 28 892.+) .g-62 588@ .2 2A, /.2.r

:2,K IC a+) w %=%bh a.^ w $=xch 68 F6, y%XJz:2,K #C N+),.- 8- N8*.-+2AB+1

:2,K dC :,2 . -,.68).95, Z+/2AC 5,v PYw%=#Rh -+*A2 PYw%=JR

:2,K $C j w IxdcX 68 )8-B.5+\, _8- j .)/ YC -,/ 685+/ PYw%=#Rh95F, 685+/ PYw%=JR

"^.BK5, 8_ A8Z 28 !8)62-F12 . L+628*-.B

8/10/2019 Lecture1-2407.pdf

13/27

T/,.6 9,A+)/ B.@+)* L+628*-.B6

MA, ^(.^+6 /,61-+9,6 2A, /.2.{6 .12F.5 B,.6F-,B,)26h MA, 3(.^+6 /,61-+9,6 A8Z B.)3 8_ 2A, B,.6F-,B,)26

_,55 +)28 ,.1A -.)*, 8_ /.2.h

j8-B.5+\+)* 68 2A.2 2A, .-,. +)2,*-.2,6 28 \,-8

.558Z6 F6 28 F)/,-62.)/ A8Z 2A, /.2. +6 /+62-+9F2,/r

MA, F6, 8_ A+628*-.B6 1.) .+/ 18BK.-+68)6 8_/+m,-,)2 /.2. 6,26 8- B,.6F-,B,)26 .*.+)62 ,.1A82A,-=

MA, F6, 8_ A+628*-.B6 1.) .568 A,5K 28 /,2,-B+),C "BK+-+1.5 W-,[F,)13

8/10/2019 Lecture1-2407.pdf

14/27

7F|)* MZ8 L+628*-.B6 :+/,(93(:+/,L,-, +6 . ;'(5$(1#($8_ 2A, /.+53 .S,-.*, -.+)_.55 +)

8F- -,*+8) PO,/R .)/ :+)*.K8-, P?5F,R= N,2 F6 F6,A+628*-.B6 28 588@ .2 2A, /.2.r:2,K IC a+) w %=Iha.^ w II#=bh

68 F6, y%XIIdz:2,K #C N+),.-8- N8*.-+2AB+1:2,K dC :,2 . -,.68)(.95, Z+/2AX Y w I

:2,K $C j w b%JJ .)/ YwI= j8-B.5+\, 28 A.S, 2A,_8558Z+)* 2Z8 1.6,6C ?5F, P:+)*.K8-,R .)/ O,/ PO,*+8)R=

8/10/2019 Lecture1-2407.pdf

15/27

L+628*-.B :FBB.-3CL+628*-.B6 .-, . K+128-+.5 8S,-S+,Z 8_ 8F- /.2.X .558Z+)* F6 28 K8Z,-_F553C *,2 .) 8S,-.55 _,,5 _8- 2A, /+62-+9F;8) 8_ 2A, /.2.C A8Z BF1A 8_ 2A, /.2. 5+,6 8S,-

ZA.2 B,.6F-,/ -.)*,X +=,= 9,2Z,,) y} .)/ }~Yz /,2,-B+), ZA,-, 2A, /.2. +6 18)1,)2-.2,/ P2A, B8/, 8- B,.)R /+6K,-6+8) 8- 18)1,)2-.;8) 8_ /.2. P/+6K,-6,X /+S,-*,)2X 8- S.-+.)2 2A, /.2. +6R A8Z 2A, /.2. +6 /+62-+9F2,/ 8- 15F62,-,/ P+6 +2 8), *-8FKX 2Z8 *-8FK6X ,21=R

6@,Z),66 8_ /.2. P)82, 2A, /.2. A,-, Z.6 [F+2, 6@,Z p B862 8_ 2A, /.2. Z.6 .258Z S.5F,6X 9F2 . _,Z 1.6,6 A./ S,-3 A+*A S.5F,6R B+66+)* -,*+8)6 P.-, 2A,-, .)3 K.-26 8_ 2A, /.2.6,2 2A.2 Z,-, B+66+)* 8- ,BK23Ro

j82,6 8_ !.F;8)CI= O,B,B9,- A8Z,S,- 2A.2 T_ -,18-/,/ /.2. 8_ . S.-+.95, ,^A+9+2 61.U,- 8-

/+6K,-6+8)X 2A, 8), BF62 2-,./ 1.-,_F553= MA,-, .-, ;B,6 2A.2 2A, F)/,-53+)*K.U,-) 8- S.5F, 8_ 2A, /.2. 1.))82 5,./ 28 S.-+.95, K-,/+1;8) 8- 62.;6;1.5

-,6F526 Z+2A 1,-2.+)23=#= T) 82A,- 1.6,6X ,S,) ZA,) 6F1A K-,/+1;8)6 .)/ -,6F526 .-, .1A+,S.95,X 2A,3 .-,6;55 +)A,-,)253 -.)/8B= :F1A S.-+.95,6 .-, @)8Z) .6 -.)/8B S.-+.95,6X .)/ 2A,+-+)2,-K-,2.;8)X .)/ S.5F,X 1.) 9, K-,/+12,/ 8)53 Z+2A .) .6681+.2,/ K-89.9+5+23=

8/10/2019 Lecture1-2407.pdf

16/27

T)2-8/F1;8) 28 7-89.9+5+23What does probability mean?

Probability is the numerical measure of the likelihood of an

occurrence of an event relative to a set of some or all

alternative events.

Probability has two important components: identification of a specific event of interest

identification of the set of all possibilitiesrelating to the

specific event of interest.

It answers the most basic question:

How do we assign a quantitative number, value, or likelihoodto an outcome which is possible but not guaranteed?

8/10/2019 Lecture1-2407.pdf

17/27

"^.BK5,C O8|)* 4KK5,6

8F KF-1A.6, $ .KK5,6X .)/ .-, 285/ 28 .66FB, .)3 *+S,) .KK5, A.6. J%] 1A.)1, 28 *8 9./ .v,- . Z,,@=

IC YA.2 +6 2A, 1A.)1, .55 $ .KK5,6 .-, Gf .v,- . Z,,@o

#C YA.2 +6 2A, 1A.)1, d .KK5,6 .-, Gf .v,- . Z,,@o

dC YA.2 +6 2A, 1A.)1, 2A.2 # 8- B8-, .KK5,6 .-, Gf .v,- . Z,,@o:2,K IC T/,);_3 .55 8_ 2A, K866+95, 8F218B,6=

T) 2A+6 1A.-2X u B,.)6 2A, .KK5, +6 *88/X ZA+5, ? B,.)6 2A, .KK5, +6 9./CPuw$X?w%RC uuuu

PuwdX?wIRC uuu?X uu?uX u?uuX ?uuuPuw#X?w#RC uu??X u?u?X u??uX ?uu?X ?u?uX ??uuPuwIX?wdRC ???uX ??u?X ?u??X u???Puw%X?w$RC ????

8/10/2019 Lecture1-2407.pdf

18/27

"^.BK5,C O8|)* 4KK5,6P#R

I -,[F+-,6 2A.2 Z, A.S, $ u{6# -,[F+-,6 2A.2 Z, A.S, d u{6d -,[F+-,6 2A.2 Z, A.S, # u{6 ~ d u{6 ~ $ u{6IXd w Puw$X?w%RC uuuu#Xd w PuwdX?wIRC uuu?X uu?uX u?uuX ?uuu

d w Puw#X?w#RC uu??X u?u?X u??uX ?uu?X ?u?uX ??uuPuwIX?wdRC ???uX ??u?X ?u??X u???Puw%X?w$RC ????

:2,K dC F.);_3 .55 K866+9+5+;,6 .)/ 2A,+- 5+@,5+A88/=

:2,K #C

8/10/2019 Lecture1-2407.pdf

19/27

"^.BK5,C O8|)* 4KK5,6PdR

I -,[F+-,6 2A.2 Z, A.S, $ u{6# -,[F+-,6 2A.2 Z, A.S, d u{6d -,[F+-,6 2A.2 Z, A.S, # u{6 ~ d u{6 ~ $ u{6T) 2A,6, 1.6,6X +2 +6 )82 K866+95, _8- 2A,-, 28 ,^+62 B8-, 2A.) I K866+9+5+23 .2;B,= L,)1,X 2A,3 .-, BF2F.553 ,^15F6+S,=

:2,K JC MA,) +) 2A+6 1.6,C

:2,K $C

8/10/2019 Lecture1-2407.pdf

20/27

"^.BK5,C O8|)* 7,.-6P)82, 6+B+5.-+23 28 .KK5,6VR

8F KF-1A.6, $ K,.-6X .)/ .-, 285/ 28 .66FB, .)3 *+S,) K,.- A.6 .b%] 1A.)1, 28 *8 9./ .v,- . Z,,@=IC YA.2 +6 2A, 1A.)1, .55 $ K,.-6 .-, Gf .v,- . Z,,@o

#C YA.2 +6 2A, 1A.)1, d K,.-6 .-, Gf .v,- . Z,,@odC YA.2 +6 2A, 1A.)1, 2A.2 # 8- B8-, K,.-6 .-, Gf .v,- . Z,,@o

:2,K IC T/,);_3 .55 8_ 2A, K866+95, 8F218B,6= P6.B,R:2,K #C

8/10/2019 Lecture1-2407.pdf

21/27

"^.BK5,C O8|)* 7,.-6P#R:2,K $C

8/10/2019 Lecture1-2407.pdf

22/27

:,2 MA,8-3

M8 K-8K,-53 _8-BF5.2, . K-89.9+5+23 K-895,BX Z, BF62

/,g), 2A, ,S,)2 8_ +)2,-,62X .)/

2A, 6K.1, 2A.2 2A+6 ,S,)2 2.@,6

:,2 MA,8-3 *+S,6 F6 2A+6 2885V

:.BK5, :K.1,X Bp 6,2 8_ .55 K866+9+5+;,6 g)+2, 8- +)g)+2,h /+61-,2, 8- 18);)F8F6

"S,)2X Jp . 6F96,2 8_ B

!8BK5,B,)2.-3 "S,)2 Jp 2A, 6F96,2 8_ B6F1A 2A.2 +2 +6

,S,-32A+)* ,^1,K2 _8- J

jF55 ,S,)2 Kp )8 ,^+6;)* 6K.1,e.) +BK866+95, ,S,)2

8/10/2019 Lecture1-2407.pdf

23/27

Q,))

8/10/2019 Lecture1-2407.pdf

24/27

:,2 MA,8-3 ( N8*+1.5 GK,-.28-6

MA, B862 9.6+1 8K,-.28-6 P58*+1R .-,CI=

0)+8) P8-R p4-,. 8_ +)2,-,62 18S,-,/ 93 ,+2A,- ,S,)2

#=

T)2,-6,1;8) P.)/R p4-,. 8_ +)2,-,62 18S,-,/ 93 982A ,S,)26

2

!

!

L

A! B

"S,-32A+)* )82 3,558Z+)6+/, 2A, 98^ +6 *+S,) 93C

MA, .-,. +)6+/, 2A,/.6A,/ 98^ +6 *+S,) 93C A! B

8/10/2019 Lecture1-2407.pdf

25/27

:,2 MA,8-3 p OF5,6 PIR

4R

7-89.9+5+23 BF62 .5Z.36 9, 9,2Z,,) % .)/ ICI 7PJR %

?R

7-89.9+5+23 8_ .55 ,S,)26 811F--+)* +6 IC

7PBR w I!R

aF2F.553 "^15F6+S, ,S,)26 .-, C*8(A(*8(*)FXG1)"&+&*/3FX 8-A1&03-8#*+= MA,-,_8-, 2A,3A.S, )8 8S,-5.K=

T_ JM.)/ JN.-, aF2F.553 "^15F6+S, 2A,)C!

JM JN

7PJM JNR w 7PJMR ~ 7PJNR

8/10/2019 Lecture1-2407.pdf

26/27

:,2 MA,8-3 p OF5,6 P#R

8/10/2019 Lecture1-2407.pdf

27/27

:,2 MA,8-3 p OF5,6 PdRLR "^2,)/+)* ! .)/ u 28 2A-,, /+m,-,)2 ,S,)26C

YA,) jGM a0M04NN "}!N0:TQ"C7P R w 7P4R~7P?R~7P!R

(7P4?R(7P4!R(7P?!R

~7P4?!R?F2 ZA,) a0M04NN "}!N0:TQ"C7P R w 7P4R~7P?R~7P!R

A! B!C

2 L

A! B!C

O7P4?!R