U1.U I. Gaylord, Michigan. Friday, Mar. 13, HELD A QUIET ELEUi IUN. Only Fifty five Ballots Were Cast at the Election on Meaday last

Size: px
Start display at page:

Download "U1.U I. Gaylord, Michigan. Friday, Mar. 13, HELD A QUIET ELEUi IUN. Only Fifty five Ballots Were Cast at the Election on Meaday last"

Transcription

1 3 ( ER «0000 ( ( $25 25 N $2 $4 2«0 N RD X E «?\ ) «! (} 9 x «0!! GERGE PRE D G «N NDY EE R G x D K K P!! 7 G K P P R x E K«8 R E \ $ « $ «!!! «Y 2 23 D ;; & R NDRN RE GD N ED QE EE N E REE RN N N E K ««««» x EE RRD N 32 D D G Q E P»!! / \ x x Y 4 RDE & Q G EQ P P E & E 907 D P x E Q D EENNG E P E ~ K R G R «K «! ; Q R x G» P $ «( < %%%%% %»»% % %%%\%«%\\«%«%% RE Y GNG D! NYNG? P P R Y & P %%««%\«%\x %%%

2 »»»» » «»! + G! P! P KX P EER RRNGN x R DRE NN! P E [ 907 G R ]»»»»»»»<» NER PRYNG D? P»+»«<» Y N D P »? <? G D P 0 RDE x; E D? P ~ \!» P P D G N P ; x! P P D? D P? Y? N! N D < Y D! R?! x P? 7 x P N D? x Y x N P D?» <»! <2 D! x! x N! P? E!! P x P P x D! Y? Ex / » ~!! E X»» KK x < N x»~ N x N» «!» Q } P N! P «Z? x! «! K % K \!;! E! P!!!! »» K D?!! G Y x P K? EKR x! PPE E P x D D! E Y ~ P x P D E? Y? «D &? E! P? D P!!! P? P x N E? P D P! x?! D EXPN D? E «R XKN N!!?? N Y!!?! ; E P xx»«!! < {? «7 Z E ««x»»» ««Z D P x Y P D K x D? P G N ;? G x?! ; \ ;»? P Y? E! P ;! x? P N < N! D? 9 ~ 7 » < < x? x»«;;;; ; ; ;;; N P N E??? R D D x N «?! Y Y Y 4 x» «!! ( x x D ( Y Y! E? N D ) )x R!? P» ; P P x < x! x» (»««<!»<! P G G R G E RP P 9«/ Y R P ER x» K x (] ~» D D! x NE EN K % «P K E D»«) x GE P G ~»»»; x»» ~»»== R! K «( ««5? ( D 8 0 E P ; E? < «P G G R R P G K E K!? N? G x 9 K 2 & ; 8!! 9 x K x «G R E E xx ; N K E P ; ««< E E P R G < ; D PGN K! «# <»»? E P x «x 3 x x N 8 G DRPED DED 8» x ( P R x N E E P < 4 4 x ;» P R N <% E E R DEYED G & G K N 6 N K 3 P Q x K? x ;!; «5 $5 80 ; D x N \ KED XP G E P ( $5 00 D 9 R x x Y $ D P «! D x» x 4 D P < E 8 Y 3 D N? P x x G K &» 2??!»» \ RN N x ; x R x x ; < «? PN«X RN \ Y? 9 x K? ( N ; N E «x < x N» E N KKD RN P! E G G G 00 % $! ; $ Ex P EEPNE 6 E»»» «««~!!!2»(«««Kx»» «P 0 D P& G ( E Y x x 0X»0 P! 907 D x N K x! [! x»» 6»» «»<? 907 P 2300 ) P [ E N x P N D»9 N 97 P »24 ; 002 Ex 79 P N « K«~%~ » E EXPDED N ND K R D R E NE ND PRE DRG P E ERN DNE DNNG E PN NGER

3 GN PE P G «GENN R NER E P R N E D R E G \ P P G E P P 400 E»»» K» «P K («8 D P ; R» % & K D GD RD E E YR RPN x P R[? <; < x G K P EG NY E x G P R «x Q«(!«< < G ««R K E «««««~«! R ERE 20 R E P 0 N E D R ;; ; ; ; «R 20 x x ; KNE KKEE G NEY X «D» E x # x ; x x ; x 0 x D R E Y E x x 0 \ K K <»«~ < «0 N»» x»»!#» 0 D «x »» «( «E P x G K P G x G RE PNGNN8 DKRK R G PYN ND QE x G PY8N ND RGEN G 4 08 N ENKE RED R \ X DNG R P!! K!! x G «DEN K 8 x G E EER PN E 2 G 75 « »» / K /»»» E /! ( RED KNG #» X DNG K D PYN ND RGEN EG 3 E ; E! 7 8 R G x E x D N $ 00 $ E G 5 9!» x 0 ««/ ; EXPERENE PYRG 22& «««<< N EZE x R N G D NE DR ER x D E < Q D D N K 3 Dx E K D N ~»»»<» 22»« G 2 4 P x 2 2 \ 3 x D» ;»«~» K P Y 25 x # D 300 D 4 PR R D P E EENG P E D 4»<»~ R # «G» G 4»»»«( < <»» E x R R! E R» GE ENGNE R E D R»D( E «x ( 3 5 G N 3 0 «Y K KK R R»»?? $ N! KK PQ ; 2 RKERY N ZR 600D R EXN K» R N 8 D K D» 0 K x ZDXD P G E # Q P»» D E Y ; RE R NR YER D E NNN Y YNG N /! ; ;! K ] P E QR/D 32 DE P N REE R $ Y EY DEP XE R REN Y } x x N R D R<K <<«Y N ;; Y G EENN EEER ND PN GRR & N D G K D P x K R P P R EN GYRD E N6 NK K < \ x ; 5 0 «PRRR K 22 P 2 K P 8 3 P \ N Y x G P «<! ;! ) ; «! D K & 3! P 3 N N P 76» ( «P R P ( D P NRY P P P P P P 4«P P P < P!) ; P ; ] ; x P ( Y R K R P 85 P P ; ; R R 908 NY N x ; P!!!! P K! P ] K < 0 / N \ ; ; 0 ( G X \ \ D P 5 08 P G K Y 2! x Y G X K P K E P P ;!! «P x xx G G 0 & P R K E «K 2 x P P Q \< \! N0E G N ( R G 4 4 «KDDN DER NRNE RE EE P 52 GYRD GN «K 6!«N P N Q@» P P / ] PN GZNE 0 Y0N D & Q G G «E PYN ND RGEN NY N P 9 G R D P P P 2 G 2 4 G G N 22 R E? & DEN R 8 GD R E E R Y D Y N R!! E E 5 0 D R D E RE Y N G? 22 x x \! ««)! «D < ; P x P K x «x ~»»»»» P P! «x «! / P \ \» \ P R P < ) G «) x» K» \»» # R» «N»» ; ++ «P P «x<» 3 ; ««K ;» «» «P «< N E EG NY NK $\ $

4 E NDER E P x x \ x x Y R Y ND G P ; \! x P K E 2000 RE P P Y Y $ P E E D 7 ( <x 3 PRNG K G K G Q x P 8 N «x ~?«P Y «K (! K x D 48 x «K 48 Y x ( 4 5 x! x ) Y K R E NDDE R NP RERER 3 K NG XX RPx G G Y»»!!! 2!! x «) 4&Q x \<! ;;! N E KN E N ND RE P G ( N D ( R NP 8 6 E D R R 24 ; R G D E N Y x N P? & P P G D x Y + D N D G G 5 x»/ NG RE R P» D K R» D K» K RNK RNDP x & Y x Y D D NGREGN G 00 N ) K 2» G D ~ E 30 E 730 R Q % <» D««P «» «;»; «; 6 /»» «; «< D 30 G D & ; N P $ 00 N D D x & < \ D R ; Z ; D 2 G D P D Q D K x R 2 0 x x 33 K < \»» E & P ; N Y 3 5 G G» 5 x»<«««««; ;«! <(» 3» ~ & P K ~<! «« R Ex \»» $ 2 5 RRNG!» «R 00 P D 227 $ 8 5 P 9» < P N K? Y ( x N D D E R NP < G R E R E R R R RNER $500 D G K! x Y Y ; E x G «R < x» E / N P 2 4 P x ) { ( Y! % ;;\ ; ] ( D ) ] P «\» «P 29 P R N» R! E P G! G 0) x N D x x «P \ ~ x «««K) G D D? P K& x 7KGR < P X P ;»» 9 R DEDED RNRE G E G G DN + R R E 4 R Y R Q RE G GN & N N N ~~ Y N REPN R NP ERK E DEPR EE NK RKE DRG E GERGE PER PEN RPRE \ N RN ] ] NDER EX N NEER N»\» x» K x D / Y P RER N» ~ \ N 9/9 Px / R5 P Y R E! (!» E R DE RE XED D NEDNG K! x» x» \ ~ x Q x! N x x PRN Y R E RRY PEN D 8 5 P R x NP RERER N «Q P N ) x x x x x G R Ex R P x G x G 8 D 8 x P RDY P R 4 E DY R E N R E N x «) x } N 8!05 x < < x «; ;! x R ERE RR NE P»» DERED~EER P K P K P G NNERG 8 G ) «! G G \» P D D P N»» D ] D G K x G P G G G 3 5! )< D ; «0< 00 $ N # $ )0 $ D K $ ) N D ; $ $000 D ««P ) P? x»! P E < x «/» & E PPENNG N E P R Y NE EDN [ ]? K ; ; P» ) N ND RRDR G P $ ] 7 / N P G \ <! K G K 4! x x ) x ) x x? 0 x ] D N \ \ Y P E x! Nx P N G»» x K N x x K x K!! «? x»»»» ; [] \ x» K ;! D 3 2 Y < \?? «K x! ; ; x < N x D x ] 2 K? x x Q N 5» N ER ER Q ( ] Y «N E N «! ; ; Q x ; R x! N!!! x N»?!! ««!» ;! ;;;; \! \»? R»? ; <( < x ;; ] N <»! ] x \ K ««R ; < PP! x» ) ««««Q «# x x P x E DN EN NRN ~ «EE ;

5 N XE $! 009 ENE EE P EXE ERE P 0 NE E N P R / R G 2 6 D 90 R (»)! «; (2) ( P ) x (22) E (9) x G ( ) 27 x D 2 D 8 G E R G E K N E N D G P P Y 6 E 70 P 00 P P R K «256 E PR 5!!! G =K G G E N N D GD EERYNG NE G R NER RDE ED R R E P P E 600» K P E GN EDE R R P 8 $ G 26 E P ;; D P! 47 E P P R K R K P!;; ; 0 R D 22 < G R 0 D 29 D xk 23 ( G 8 R K N N E K G Y R D RDN NGREGN EN R R P x x / E G x E R E N x 9 P P K ; x N R Y E GN G D P» 700 K N E E DR NE 0 G 3 N P R E 4 D « N D 600 Y P E E N G P RNE ND RE GD 7 3 EEK NG <» D G 8 00 $! $0 $200»( R! X R D!» P ; & E 0 x 3 0 x NK EN 2 E R E N 6 0 P < E E K K N E R D x 4 K E R N ; ; x ] G x x x NE! G E E D» G RED NE /4 D K N EN» «# 0 K «N \ E N\D NE KX E» 0 \» N E DE 0 RK RKE RE ) x K N K 4!«D N! REPN EKR» P «/ KK 4 «< K E GN < 0 < K P R» «] ; «x < K R 0»»! ( N N 4 K E» 5 N «7 \ # K K / N EN 5 { < 5» \ N P < \ D K NK K N» 4 E E RRD 6 ;» 0 N » < E P N»» 2 K P»! 4 ; «N» E <! ( x!~\% REDER \ %! P! K \ x 2 P 5 «R E D R»< ; < «R \ Y» K ] < 0 P \ < \ \» \ \4 N 2 \ \ ; ««! < E ] ] < / 4 «< ««4 \ [! ;» G K N ; \» \ ; N / ; K! < < «G ( \» < R» E D D Y REGRE DEY E E GRERE R GNER E PEE R ER 7 RN RD & R 73 «/ D «K #» ; EK D P G RKERY GRE N Y GE K EDN PNGRP RERD GN ENR! E

THE WEATHER f. Rain,' colder by night. New Jersey Advocate APPEALING! BENEFK VOL. XVIII. SERIAL NO Among- Those Present SIOUN AUTO CUPS

THE WEATHER f. Rain,' colder by night. New Jersey Advocate APPEALING! BENEFK VOL. XVIII. SERIAL NO Among- Those Present SIOUN AUTO CUPS P PBED E EEY RY ERE E EER RY E G R E G D 0 Z R P E R P E E D PPEG BEEF X ER 200 RY Y EDY FER RY 22929 R EYREEE D FR PE GRERE P GR RYD R z BG F x DER G EXGGERE x 3 B 6 / ± P B FREE DEERY RY E RE PPG EER

More information

A L T O SOLO LOWELL. M I C H I G A N. T H U R S D A Y, M A R C H THE ADS Board of Education FOR YOUR GAIN

A L T O SOLO LOWELL. M I C H I G A N. T H U R S D A Y, M A R C H THE ADS Board of Education FOR YOUR GAIN W ED R DRVEN N YER P EDWRD R WE ND JE R R V RNG DEN EG DREN E RN ER ER E J WE G N R D Y R 2 932 VE XXXX N RED WE R W E D E N PPER x 6) R YR GN WRNNG DE Y PERN N NEW EE NEq ENE8 VERED N RPED ENDEN NG PRPERY

More information

Monday, July First, And continues until further notice.

Monday, July First, And continues until further notice. 4 E N % q * - z P q ««- V * 5 Z V E V 3 7 2 4 8 9 E KN YNG P E K G zz -E P * - PEZZ 23-48 G z : P P 78 N P K - - Q P - 8 N! - P - P 8 8 E E-*«- - 3 4 : G P - G N K P P Q* N N 23 E 2 *8342 P 23 2552 2K

More information

('(IMMr.lti'lAb I It I TI'J ;i tnn t - ' ".rt.r- - ; lire-- K. !llolplll fir on square, f r :h spice f J lir.e,.--, r quarter HAWAIIAN ISLANDS

('(IMMr.lti'lAb I It I TI'J ;i tnn t - ' .rt.r- - ; lire-- K. !llolplll fir on square, f r :h spice f J lir.e,.--, r quarter HAWAIIAN ISLANDS P ER N R b P 50 z N P 0 b b x E 0 N 0 x N E b N R P N N b b N N P 00 N x 50 b G 6 b N P R x 0 b 5 z N b b b b N b D E N x b b b b b b D b Y N b b b E E D b z P b z b b b R b Pb R b Ez Px P R P b b b P

More information

Adver-isemen- suliber, 8 nries) PLAIN AND FANCT. forrip Sailora. starts, gtorlling5,'tv.to 'gtl. Waikiihalulu Water Lots! LARGE AND COMMODI- -,

Adver-isemen- suliber, 8 nries) PLAIN AND FANCT. forrip Sailora. starts, gtorlling5,'tv.to 'gtl. Waikiihalulu Water Lots! LARGE AND COMMODI- -, E E ERER RER p p p p x p $ p 0 p xp p p p p p p E p q 0 $ p 8 p $ 0 $ E EEER Y R ER 8 E 8 8 p EERE p p p REEREE q 8 Y p p p REEREE x E p Eq R p RE ER ER p x q EE p E E GR G p p 0 0 0 0 p x x p x p q EER

More information

HEAGAN & CO., OPP. f>, L. & W. DEPOT, DOYER, N. J, OUR MOTTO! ould Iwv ia immediate vltlui. VEEY BEST NEW Creamery Butter 22c ib,

HEAGAN & CO., OPP. f>, L. & W. DEPOT, DOYER, N. J, OUR MOTTO! ould Iwv ia immediate vltlui. VEEY BEST NEW Creamery Butter 22c ib, #4 NN N G N N % XX NY N Y FY N 2 88 N 28 k N k F P X Y N Y /» 2«X ««!!! 8 P 3 N 0»9! N k 25 F $ 60 $3 00 $3000 k k N 30 Y F00 6 )P 0» «{ N % X zz» «3 0««5 «N «XN» N N 00/ N 4 GN N Y 07 50 220 35 2 25 0

More information

fiff w 4h WEDNESDAY JULY 23 1SS3 COMKCTIOXKHVI 4 4Ty X 41x1441 as x n rcnsut4 Hotti su KEEPS ALWAYS ON HAND A4 HMlwll l4 Vlt I W

fiff w 4h WEDNESDAY JULY 23 1SS3 COMKCTIOXKHVI 4 4Ty X 41x1441 as x n rcnsut4 Hotti su KEEPS ALWAYS ON HAND A4 HMlwll l4 Vlt I W z RR GR NN N 5 P R d P N N F N Q d R F d d Z D d Q d 5 d g R P 9 g F d g N 9 Q R R F F d z z 5 P 9 d RNY N DRD F R G R 5 R 5 R 5 D N N d N RN N Z R P P P 8 D 5 5 z Z g 5 YY d R F G R R N 5 d D D F P Y

More information

ards tifferkuiitat ED C BOWE House and Sign Painter Paper Hancr etc Silr Xo 1W King Slrset Ilonolnln S VJI JOIBS Morolaant Tailor

ards tifferkuiitat ED C BOWE House and Sign Painter Paper Hancr etc Silr Xo 1W King Slrset Ilonolnln S VJI JOIBS Morolaant Tailor RR R FD5 D b70 z x 25 27 b p b b pp g p p p b p b b p b p b 3 p p N b x p p b p 6 F R 2g g b p ppg g p b gg p 270 Z p 0 p g p p p b R 60 g pb 25 p bg p pp p g g g g xpg p 6 b b pp g g g p g p p g p p b

More information

INDEPENDENT IN AM, THINfiS. NEUTRAL IN NOTHIfSfi

INDEPENDENT IN AM, THINfiS. NEUTRAL IN NOTHIfSfi * * NDEPENDEN N N NEURL N N YL N 36 LELL N 2 99 LE N 296 N LL P R $0 DY--K *Y " - R YLN 3 R YLN N R 47 R [47

More information

I ' l A MEMPHIS, TENN., SATURDAY, AUGUST 23,1873.

I ' l A MEMPHIS, TENN., SATURDAY, AUGUST 23,1873. - P G& P P G» -» - P D - RP P R G GFFX G - 3 D G» R» G - G > D X >»» P -3 8 7 3-379 ( -» - F X P X X z» FR 0- P x X >»» P»( > ( 3 - - --5 - X- - x 25Z3 - - z - 37 - x -» x V5?» - > 3 x & 2» x z > - -»»

More information

MIS S BALLS, L.L.A.]

MIS S BALLS, L.L.A.] & N k k QY GN ( x - N N & N & k QY GN x 00 - XX N X ± - - - - ---------------- N N G G N N N Y NG 5 880N GN N X GN x ( G ) 8N ---- N 8 Y 8 - N N ( G () G ( ) (N) N? k [ x-k NNG G G k k N NY Y /( Q G (-)

More information

'irv:, -- bbctiisrr. MrMrMS. ri'r. la The DKCEMBER M, Hltrbirial. Barrel Factor; Shop on Fort St., opposite Hipper' FIRE INSURANCE COMPANY,

'irv:, -- bbctiisrr. MrMrMS. ri'r. la The DKCEMBER M, Hltrbirial. Barrel Factor; Shop on Fort St., opposite Hipper' FIRE INSURANCE COMPANY, E PP B p N P 7 p P E pp pp P p 7 P p p pp p p p B 2 B R B p? E N? Y B Y p R Y p ) N RE 75 6N B ) N E ) 0 NGN PR E BRN GE PGE B 7 RER Q 7 RGEN N PN B ) E RRG ER E E BN EN ER RER N PRER N N EE BREER NG EER

More information

Commercial I'l Ill icit IS PUBLISHED Kvery Saturday. 3T. p. e me..ar-- s, HONOLULU, HAWAIIAN ISLANDS, FEBRUARY. LtW'J. CLSTT. WHITMi. C. W.

Commercial I'l Ill icit IS PUBLISHED Kvery Saturday. 3T. p. e me..ar-- s, HONOLULU, HAWAIIAN ISLANDS, FEBRUARY. LtW'J. CLSTT. WHITMi. C. W. E P P b PBED P b N x DD N G b Q b z b b b b E RERY EED PRER b b b b b b b b b E b b GRN ER P x b P b b G b P bb b q bb x B b b b b b b b b E q z b b b b b x D PR b b b b b b x b b B b b Nb b b x b b Nb

More information

THE LOWELL LEDGER. X

THE LOWELL LEDGER. X * : V : ~ E E EGER X Y X 22 E Y BK E G U P B - ; * -K R B BY K E BE YU YU RE EE «> BE B F F P B * q UR V BB«56 x YU 88»* 00 E PU P B P B P V F P EPEE EUR E G URY VEBER

More information

'Xomincrcial (LciiuiuTciai. It II. J XV' tct if. II. II ei siaaspa. card, a ill VOL. 313niral... Cooper and Ganger, at the Old Stand, KINO AND

'Xomincrcial (LciiuiuTciai. It II. J XV' tct if. II. II ei siaaspa. card, a ill VOL. 313niral... Cooper and Ganger, at the Old Stand, KINO AND ux DY DK D K u NG K D R RK Q GN b u b b D K u u u x xu b b b b x RRD KRN RK R u K K u u x RN K b u RN ND GN N N G KN u Kx G G u b u bb u u b N bb x u x Qu Kq 9 D R RN Rb N bu u NYR G u N QN NRR Ku 9 R

More information

'g$-y- )4r0---aooaOC- r. o. A9.Heo'i.OMaoa)a.9. w?s. R ; : ; 09a:.aaa'. L31ia. a.j-rf-boam- WaTaB Z. rf5. ,at. f2 OOMS09r.)tafi.aaatrnvrtt.f.ai. l"s!

'g$-y- )4r0---aooaOC- r. o. A9.Heo'i.OMaoa)a.9. w?s. R ; : ; 09a:.aaa'. L31ia. a.j-rf-boam- WaTaB Z. rf5. ,at. f2 OOMS09r.)tafi.aaatrnvrtt.f.ai. ls! P K PD K D 0 D X P P Z $ X P R YR D z x R x P K 0 K x K K 0 x 0 0 0 0 0 Z x 0 0 0 0 0 x x 0 00 0 P 0 K K 0 0 0 K K 0 0 0 K K X G Z 0 0 0 K 0 0 P x x q P x R 0 0 K0 x q x P 0 0 P G 00 R 0 K x 0 0 0 Z 0

More information

Mathematical Induction Assignments

Mathematical Induction Assignments 1 Mathematical Induction Assignments Prove the Following using Principle of Mathematical induction 1) Prove that for any positive integer number n, n 3 + 2 n is divisible by 3 2) Prove that 1 3 + 2 3 +

More information

LOWKLL. MICHIGAN. WKDNKSDAV. JUNK is, IS7I. M ' M r. F. n. v j. 1,(1 W . NATIONAL BANK I I P ' O F L O W E L L.

LOWKLL. MICHIGAN. WKDNKSDAV. JUNK is, IS7I. M ' M r. F. n. v j. 1,(1 W . NATIONAL BANK I I P ' O F L O W E L L. G B L? -- LLL GN N N L \ L BY- B RB & N (» R BRN - 2 R RNG N» _ 8» B - < - B -»q $ 28q \ 2 2 2 8 2 R 2 2 B - B 2 B N q B Y N B (» -» - L ( \ ( \ N N - Q B - - B - / - B - - R B B & LR8 } ( B B G B NR q

More information

flbc in Russia. PIWiREE COHORTS ARE NOT PULL- ING TOGETHER. SIGHTS AND SCENES IN ST. PETERSBURG.

flbc in Russia. PIWiREE COHORTS ARE NOT PULL- ING TOGETHER. SIGHTS AND SCENES IN ST. PETERSBURG. # O E O KOE O F Y F O VO V NO 5 OE KEN ONY Y 2 9 OE NO 265 E K N F z 5 7 X ) $2 Q - EO NE? O - 5 OO Y F F 2 - P - F O - FEE > < 5 < P O - 9 #»»» F & & F $ P 57 5 9 E 64 } 5 { O $665 $5 $ 25 E F O 9 5 [

More information

and A L T O SOLO LOWELL, MICHIGAN, THURSDAY, J U N E Farm Necessities Off State Sales Tax list Now Exempt

and A L T O SOLO LOWELL, MICHIGAN, THURSDAY, J U N E Farm Necessities Off State Sales Tax list Now Exempt H DG N Bg G HN H ND H NG g g g g Yg x x g g gg k B g g g g g g g g g g x g g g k g g g k gg g x g z g g g g k k g g g g k XY- DN H GN DP N PG P D HN DN NPNG D- H HGN HDY N 3 935 Y - H D Y X 93 D B N H

More information

TBE feahwav *'(:.*&&&& 112, KO.262S. Many Legion Officials-Si^ atuwared City clerk Wilfre

TBE feahwav *'(:.*&&&& 112, KO.262S. Many Legion Officials-Si^ atuwared City clerk Wilfre > ] ( E W R R LR >uf / u )u> N Fu < W N u W E FRDY GD RNNG DEEER 794 F u u F G 5 W 4 7 u D u u N u D q u zu x uu u u u u EQu W u u u R D u u u u u u u u D 8 ) Fz Eu x W u u u u u E R u 4 4 4 W W u Euu

More information

LOWELL JOURNAL CALLED BY DEATH, States Senator Charles H. Van Wyck, who Monday last suffered a severe Southern railway. It ran a train from

LOWELL JOURNAL CALLED BY DEATH, States Senator Charles H. Van Wyck, who Monday last suffered a severe Southern railway. It ran a train from LELL URNL V z - & Z 9 L - X Z X E R 3 0 0 LE N RL FLYNQ RN LLN N LE LLE Y E L ««U L L Ex- V N N Y 25 - L V F \V 25 Ex-U -» L & q F > *«* >««

More information

I I I I. NOBLm NOBLE NOBLE S1 JAMES CLAIMS MINING CORPORATION LTD GRID TOPOGRAPHY GEOLOGY 9 MINERAL CLAIMS LEGEND SYMBOL. 00 i. lo 0f 0 Iv SO.

I I I I. NOBLm NOBLE NOBLE S1 JAMES CLAIMS MINING CORPORATION LTD GRID TOPOGRAPHY GEOLOGY 9 MINERAL CLAIMS LEGEND SYMBOL. 00 i. lo 0f 0 Iv SO. j R m F me km P NDY R j MGNET DEN TN P v Q c P ME 8 c RBNTE d c PERMN ND PENNYVNN HE REEK GR P GEG EGEND e HGHY FTED RBNEU RGTE d GREY TE GREEN N EERVED FRM N T E FW TERED GREENTNE G v NBE NBE NBm c REEK

More information

Magic Letterland. Welcome agic. the. Letterland!

Magic Letterland. Welcome agic. the. Letterland! Mi Leernd Weme i Leernd! e 5 Mi Leernd / 2. ire nd wrie e eers. s e z e u m mpuer 3. Jin e ds nd ur e piure. 18 17 19 20 21 22 23 24 16 11 25 26 14 15 13 10 12 6 9 1 8 2 3 30 7 4 29 5 28 27 2. ire nd wrie

More information

A.dr.rwarded to foreiirti count rie will be f 7 SOperann.. rsri--.-j- -.?- .JULY. 12, lsiii).,11,111. yc:tl crst.iif. lit. J. lor Sale... Kb l.

A.dr.rwarded to foreiirti count rie will be f 7 SOperann.. rsri--.-j- -.?- .JULY. 12, lsiii).,11,111. yc:tl crst.iif. lit. J. lor Sale... Kb l. E E b g b E x Y b p p g b 2 x $ p 2 p p 6 p x b b p x p pp 5 b x b p Y Yg g pg 2 Dp g pb? xp p g G 2 p p x D D p 59 E 9pp b b x xp D p p? 8 5 2 pp E x z b x? p p Z 2 p p x p 9 p x p p EE E EY E G E p EQ

More information

JiZuan Under New Owner. Strand Makes Generous

JiZuan Under New Owner. Strand Makes Generous LDGR NR B L G LLL N P L 4 k K K D k D k > L L LLL LD G LP R LLG L PL R RRY L Lk D 4 k q? ( () D 3 L k L q Lk L L 9 k K k k NR B RL L L 22( k -z L > G k k L LBL L k --k P z D N k q k N ( - D N P? 2 P k

More information

W I T H M A L I C E T O W A R D N O N E A N D C H A R I T Y F O R A L L. " A LOWELL MM. Sent to Jackson for 30 Years for Attempt

W I T H M A L I C E T O W A R D N O N E A N D C H A R I T Y F O R A L L.  A LOWELL MM. Sent to Jackson for 30 Years for Attempt D N N N D Y F 6 KN NY G 2 89 N NG NK!? B! ( Y FB Y N @ N6 F NDD / B F N 8DBK GN B B ) F K Y Y N? x N B D B NNG = ZK N F D BBB ZN F NF? K8 D BND ND ND F ND N DNG FXBN NDNG DD BX N NG ND B K DN G8 > B K

More information

Almost Sure Convergence of the General Jamison Weighted Sum of B-Valued Random Variables

Almost Sure Convergence of the General Jamison Weighted Sum of B-Valued Random Variables Acta Mathematica Sinica, English Series Feb., 24, Vol.2, No., pp. 8 92 Almost Sure Convergence of the General Jamison Weighted Sum of B-Valued Random Variables Chun SU Tie Jun TONG Department of Statistics

More information

THE LOWELL LEDGER. INDEPENDENT-NOT NEUTRAL.

THE LOWELL LEDGER. INDEPENDENT-NOT NEUTRAL. : / LOLL LDGR NDNDNNO NRL VOL X NO 26 LOLL GN RDY DR 902 FV N ONDRFL GRO D x N Y NK LL & O OLD RDN GON ROR NR R «ROY ND R LON N V» Rx Rj K» O ««(» F R G GRLND x ( ) R OF FRND ;«QK L L RNG X R D 02 Q F

More information

.?itja&&7. r-- Tv HAWAIIAN. gusintss (Carts. K. BONDS OF STATES UNITED. Uerrhant. Cashed at. 671 ly JOHN AT LKTT, 1131 K AND CEJIEXT, grkcrr, poite

.?itja&&7. r-- Tv HAWAIIAN. gusintss (Carts. K. BONDS OF STATES UNITED. Uerrhant. Cashed at. 671 ly JOHN AT LKTT, 1131 K AND CEJIEXT, grkcrr, poite xx u ud 00 x? u u u d P) ND KK K N d P u uu 00 6 00 0 00 0 00 0 00 u ( u d ud 6 K u u d EP N DNE REz ND NENE d Pu K u REER KNK ( GREENK R K ER ND E u D P d d? NED ud) dd uu P 8 u x Kuu u u u u d 6 NE d

More information

Stillma. Uun. B. Al.'ca ha. already her cargo. - CALENDAR. Island Notes. ua.. Eo'" e"'lej- - :" THE PAOIPXC P. C ADVERTISER CO. i&tilistmtnts.

Stillma. Uun. B. Al.'ca ha. already her cargo. - CALENDAR. Island Notes. ua.. Eo' e'lej- - : THE PAOIPXC P. C ADVERTISER CO. i&tilistmtnts. B E PF B E PEE ED PBED B E PP P DEE D P F B F E F BBEE E F z z Q F E F F F G G F F D D PY B E D B B Pxx BE D B B Q D PY x E D E P D F BE D E E D E E FFE DE D P F BE D D P P G F P F Bx P B B B G FE E PY

More information

LOWELL, MICHIGAN, MAY 28, Every Patriotic American Salutes His Nation's Flag

LOWELL, MICHIGAN, MAY 28, Every Patriotic American Salutes His Nation's Flag / U N K U Y N Y 8 94 N /U/ N N 3 N U NY NUN ;!! - K - - 93 U U - K K»- [ : U K z ; 3 q U 9:3 - : z 353 «- - - q x z- : N / - q - z 6 - x! -! K N - 3 - U N x >» } ( ) - N Y - q K x x x Y 3 z - x x - x 8

More information

STA6E NO, LR. Council DeIegote Iouncit Seol. Dqte / / Re-centif. IounciI Delegote Iouncil Seol. Dqie. Sl-oging. This is noi o sionpd subdivision

STA6E NO, LR. Council DeIegote Iouncit Seol. Dqte / / Re-centif. IounciI Delegote Iouncil Seol. Dqie. Sl-oging. This is noi o sionpd subdivision S6, LR PL SBDVS ue ny D Pn umber PS5 4627 Lcqn Ln Pr PHLLP SLD 0WS wnp Secn rwn [[men 15(P, 16 & 17 rwn P e Reerence L Pn Reerence L PS524867K P re c me ubvn MG e n nnnv n n n n pn v01.1028 0L.85 SLM RD

More information

OTSEGO COUNTY HERALD TIME3

OTSEGO COUNTY HERALD TIME3 V UNY RD 3 875 U 2 7 U { ^ ««««««B NN-KD UR Y; R «5 jj /j // ; N V W ; / B * j R- 5 W 268000 U-27-3 $30000 2 000 U-27 5 W $ 5000 46000 U-27 32 $72000 5000 D V $7674 000 $2225000 $450000 - * j 25 j 934

More information

O M N I W I L L I A M P E N N H O T E L H O L I D A Y

O M N I W I L L I A M P E N N H O T E L H O L I D A Y N P N N D Y 2 0 1 8 P V N D Y P K G $70 P R P RN & NUD R y, y q x é - y y y NNN & $ 7 $300 2 x $ 1 1 $1 5 y y $ 1 0 U $ 7 * j 23% x x. Y D Y P K G $85 P R P RN & NUD R & y, y, q x é - y y y NNN & $ 7 $300

More information

Cliques in random graphs

Cliques in random graphs Math. Proe. Camb. Phil. Soc. (1976), 80, 419 MPCPS 80-41 Printed in Great Britain 419 Cliques in random graphs By B. BOLLOBAS AND P. ERDŐS University of Cambridge (Received 17 September 1975) 1. Introduction.

More information

trawhmmry ffimmf,f;wnt

trawhmmry ffimmf,f;wnt r nsr rwry fff,f;wn My 26, $51 Swe, k "Te Srwberry Cp f e Vr,, c) [ re ers 6 (, r " * f rn ff e # s S,r,* )er*,3n*,.\ ) x 8 2 n v c e 6 r D r, } e ;s 1 :n..< Z r : 66 3 X f; 1r_ X r { j r Z r 1r 3r B s

More information

and ALiTO SOLO LOWELL, MICHIGAN, THURSDAY, AUGUST 9, 1928 First Results of the 1928 Nationwide Presidential Poll

and ALiTO SOLO LOWELL, MICHIGAN, THURSDAY, AUGUST 9, 1928 First Results of the 1928 Nationwide Presidential Poll E E XXX E Y! D 22 5 Q G Y G Y D G G q - YEE 24-? G Y E x - E Q- E 7// < D D D G E G D - 2 ; - j E ; (z ; 4 2 z 5 q z: G $7 z: $5 z: $3 E G DY G 9 928 54 Y! 8! GEG : : ; j: D - DY DY G z D zz!!!-! G E DDED

More information

Exercises and Answers to Chapter 1

Exercises and Answers to Chapter 1 Exercises and Answers to Chapter The continuous type of random variable X has the following density function: a x, if < x < a, f (x), otherwise. Answer the following questions. () Find a. () Obtain mean

More information

jfljjffijffgy^^^ ^--"/.' -'V^^^V'^NcxN^*-'..( -"->"'-;':'-'}^l 7-'- -:-' ""''-' :-- '-''. '-'"- ^ " -.-V-'.'," V'*-irV^'^^amS.

jfljjffijffgy^^^ ^--/.' -'V^^^V'^NcxN^*-'..( -->'-;':'-'}^l 7-'- -:-' ''-' :-- '-''. '-'- ^  -.-V-'.', V'*-irV^'^^amS. x } < 5 RY REOR RY OOBER 0 930 EER ORE PBE EEEY RY ERE Z R E 840 EG PGE O XXER O 28 R 05 OOG E ERE OOR GQE EOEE Y O RO Y OY E OEY PRE )Q» OY OG OORRO EROO OORRO G 4 B E B E?& O E O EE OY R z B 4 Y R PY

More information

Generating and characteristic functions. Generating and Characteristic Functions. Probability generating function. Probability generating function

Generating and characteristic functions. Generating and Characteristic Functions. Probability generating function. Probability generating function Generating and characteristic functions Generating and Characteristic Functions September 3, 03 Probability generating function Moment generating function Power series expansion Characteristic function

More information

Introduction to Probability. Ariel Yadin. Lecture 10. Proposition Let X be a discrete random variable, with range R and density f X.

Introduction to Probability. Ariel Yadin. Lecture 10. Proposition Let X be a discrete random variable, with range R and density f X. Introduction to Probability Ariel Yadin Lecture 1 1. Expectation - Discrete Case Proposition 1.1. Let X be a discrete random variable, with range R and density f X. Then, *** Jan. 3 *** Expectation for

More information

i r-s THE MEMPHIS, TENN., SATURDAY. DEGfMBER

i r-s THE MEMPHIS, TENN., SATURDAY. DEGfMBER N k Q2 90 k ( < 5 q v k 3X3 0 2 3 Q :: Y? X k 3 : \ N 2 6 3 N > v N z( > > :}9 [ ( k v >63 < vq 9 > k k x k k v 6> v k XN Y k >> k < v Y X X X NN Y 2083 00 N > N Y Y N 0 \ 9>95 z {Q ]k3 Q k x k k z x X

More information

SCOUT DIRECTOR. %$*r' III uiun yunuinui TONIGHT FOR WORK. Newuk Ctititetut- Admission SO Centg. ef Mlit UHt. Oae Asmsar Riy Pretest Three Ranbtn

SCOUT DIRECTOR. %$*r' III uiun yunuinui TONIGHT FOR WORK. Newuk Ctititetut- Admission SO Centg. ef Mlit UHt. Oae Asmsar Riy Pretest Three Ranbtn ? % 9 CRC R C 2 8 [ C C FRNP CRC C C C P F P 6 & x P R R O 8> 8> F 30 C C NGC RN ZON C R P C C O ON RN OOOX P C R C P GR COC R6 C G F R R N P P 5 9 G () 930 8 0 08 FRPRN CRC R C C (G Y P 3 $3 R C C O C

More information

12d. Regular Singular Points

12d. Regular Singular Points October 22, 2012 12d-1 12d. Regular Singular Points We have studied solutions to the linear second order differential equations of the form P (x)y + Q(x)y + R(x)y = 0 (1) in the cases with P, Q, R real

More information

ird MKsKS lok ITNKI1 FISHERS CHAMPAGNE CIDER o well and f t ihtt kttmtn in IhU community can always be found on ic ai Jacob WciL No 61 Kin MreeC

ird MKsKS lok ITNKI1 FISHERS CHAMPAGNE CIDER o well and f t ihtt kttmtn in IhU community can always be found on ic ai Jacob WciL No 61 Kin MreeC q N Y 570 ppp z dg p p y b g y b p d ZZ d D d p d 7 dd d b y y g D pd d dyp d y dy y d y d y y py b p d p b p b y g y d d d d b 5 b g 8 b p d d d 8 58 y b g y by d d p b D d b 000 pd b d b d d Rd gg 700

More information

W E S T A N D N E W Y O R K. r NEW YORK > (entral * SYSTEM SYSTEM J. Effective January 14, 1939 Effective January 14, 1939 'IP" -6 " The Direct Route

W E S T A N D N E W Y O R K. r NEW YORK > (entral * SYSTEM SYSTEM J. Effective January 14, 1939 Effective January 14, 1939 'IP -6  The Direct Route e De Rue W N D W N D U W U W N D N D RNGFD N RNGFD N N W Y R N W Y R NW YR (e Y f NWYR (e v Y ffeve u ffeve u F U N N D DNNG R R V Reu e e e bbev D RfD e e; R; Reu e e e e be W U N D N ekek D N uff uff

More information

Probability Models. 4. What is the definition of the expectation of a discrete random variable?

Probability Models. 4. What is the definition of the expectation of a discrete random variable? 1 Probability Models The list of questions below is provided in order to help you to prepare for the test and exam. It reflects only the theoretical part of the course. You should expect the questions

More information

ECE 302 Division 2 Exam 2 Solutions, 11/4/2009.

ECE 302 Division 2 Exam 2 Solutions, 11/4/2009. NAME: ECE 32 Division 2 Exam 2 Solutions, /4/29. You will be required to show your student ID during the exam. This is a closed-book exam. A formula sheet is provided. No calculators are allowed. Total

More information

Lecture 5: Moment generating functions

Lecture 5: Moment generating functions Lecture 5: Moment generating functions Definition 2.3.6. The moment generating function (mgf) of a random variable X is { x e tx f M X (t) = E(e tx X (x) if X has a pmf ) = etx f X (x)dx if X has a pdf

More information

UCSD ECE250 Handout #20 Prof. Young-Han Kim Monday, February 26, Solutions to Exercise Set #7

UCSD ECE250 Handout #20 Prof. Young-Han Kim Monday, February 26, Solutions to Exercise Set #7 UCSD ECE50 Handout #0 Prof. Young-Han Kim Monday, February 6, 07 Solutions to Exercise Set #7. Minimum waiting time. Let X,X,... be i.i.d. exponentially distributed random variables with parameter λ, i.e.,

More information

and SUMMIT RECORD SUBOMT,N.'j., TUESDAY AFTERNOON, FEBRUARY II, 1930

and SUMMIT RECORD SUBOMT,N.'j., TUESDAY AFTERNOON, FEBRUARY II, 1930 PGE EG E ERLD D RECRD k P [ ~ }5 C k C [ x R FRYFR YER 5 2 C x x $ x C C C C) C x L C C C k ) X EG { EG )) 5 7 x 2) x x ) = x C Ck L R L C 5 k 3) ) ) ) 27 7 5 D 5 C = 27 E 5658 2) 53 E $5 ) LY 22 78 2

More information

n! (k 1)!(n k)! = F (X) U(0, 1). (x, y) = n(n 1) ( F (y) F (x) ) n 2

n! (k 1)!(n k)! = F (X) U(0, 1). (x, y) = n(n 1) ( F (y) F (x) ) n 2 Order statistics Ex. 4.1 (*. Let independent variables X 1,..., X n have U(0, 1 distribution. Show that for every x (0, 1, we have P ( X (1 < x 1 and P ( X (n > x 1 as n. Ex. 4.2 (**. By using induction

More information

THE PAOiriO (Commercial Slbbcrtisrr. Commercial giiberitsrr fl'bi.i.-'iik- 1 PCBLlMIED AT. pare. I tip. lio (.rioef

THE PAOiriO (Commercial Slbbcrtisrr. Commercial giiberitsrr fl'bi.i.-'iik- 1 PCBLlMIED AT. pare. I tip. lio (.rioef hh p Y E bb K E K F Y K bp h F bp h p h K hh p h b h h b p p pk p h p h b p FY h b p h b h b b b h R K K b b p RER h b X X ER h b x b h b p h b G p h b b Y ph Q h h hh h F h h h hb h pp p b h h p pb h

More information

dy dx dx = 7 1 x dx dy = 7 1 x dx e u du = 1 C = 0

dy dx dx = 7 1 x dx dy = 7 1 x dx e u du = 1 C = 0 1. = 6x = 6x = 6 x = 6 x x 2 y = 6 2 + C = 3x2 + C General solution: y = 3x 2 + C 3. = 7 x = 7 1 x = 7 1 x General solution: y = 7 ln x + C. = e.2x = e.2x = e.2x (u =.2x, du =.2) y = e u 1.2 du = 1 e u

More information

Trader Horn at Strand This Week

Trader Horn at Strand This Week - -N { 6 7 8 9 3 { 6 7 8 9 3 O OO O N U R Y Y 28 93 OU XXXX UO ONR ON N N Y OOR U RR NO N O 8 R Y R YR O O U- N O N N OR N RR R- 93 q 925 N 93; ( 928 ; 8 N x 5 z 25 x 2 R x q x 5 $ N x x? 7 x x 334 U 2

More information

Liberty unci Union One and Insep,arable. r ' LOWELL. MICHIGAN, WEDNESDAY, AUGUST 10. 1*7

Liberty unci Union One and Insep,arable. r ' LOWELL. MICHIGAN, WEDNESDAY, AUGUST 10. 1*7 LLL KL G L L LLL GN N G 7 L LLL K L K) :K : NN : N K N K K L< N L N $ K 2 NG N q 6 [ ):L NN NK L $ L KKX K N X KK NX K: $ $ $ 2 2 2 2 2: 2 < 2 2 7 L ««$ q L N K» KL L K «» K ««LK K «N «L < K 2 N NG ««G

More information

LOWELL. MICHIGAN, THURSDAY, AUGUST 16, Specialty Co. Sells to Hudson Mfg. Company. Ada Farmer Dies When Boat Tips

LOWELL. MICHIGAN, THURSDAY, AUGUST 16, Specialty Co. Sells to Hudson Mfg. Company. Ada Farmer Dies When Boat Tips K N» N - K V XXXV - N 22 N 5 V N N q N 0 " " - x Q- & V N -" Q" 24-?? 2530 35-6 9025 - - K ; ) ) ( _) ) N K : ; N - K K ) q ( K N ( x- 89830 z 7 K $2000 ( - N " " K : K 89335 30 4 V N

More information

~fw. urning Desire. lean ul. «sw. Final Extinction NEW QUIRK 69, N. Q., TUESDAY, APR^FCX^^W. ted:

~fw. urning Desire. lean ul. «sw. Final Extinction NEW QUIRK 69, N. Q., TUESDAY, APR^FCX^^W. ted: EK» - - - u I» -? NE QUIRK 69 N Q UEDY PRFCX F Ex X!E - - - ; - - - ; & P --?!R» u \ u CCNY -C C j pp N up - [ P-up p upu >j u D CC F 9u - x pu x pp p p p u p & K I? - >

More information

APPM/MATH 4/5520 Solutions to Exam I Review Problems. f X 1,X 2. 2e x 1 x 2. = x 2

APPM/MATH 4/5520 Solutions to Exam I Review Problems. f X 1,X 2. 2e x 1 x 2. = x 2 APPM/MATH 4/5520 Solutions to Exam I Review Problems. (a) f X (x ) f X,X 2 (x,x 2 )dx 2 x 2e x x 2 dx 2 2e 2x x was below x 2, but when marginalizing out x 2, we ran it over all values from 0 to and so

More information

ation and that his estimates of at the close of the present fis-' 1, He believed that $50.-

ation and that his estimates of at the close of the present fis-' 1, He believed that $50.- LWELL UNL 2 N 35 LWELL WD2ZD&7 93 D Y WLL E W x D NF W > N G WN F) WNGN F 27 x NW EE W k! U FN F 25 W k z k W ELE DEED Y W D F G FFU E LN G F 27 F k F EENEEN LLN FU WNGN F 27 F x F k W F 3 3 25! k q k

More information

828.^ 2 F r, Br n, nd t h. n, v n lth h th n l nd h d n r d t n v l l n th f v r x t p th l ft. n ll n n n f lt ll th t p n nt r f d pp nt nt nd, th t

828.^ 2 F r, Br n, nd t h. n, v n lth h th n l nd h d n r d t n v l l n th f v r x t p th l ft. n ll n n n f lt ll th t p n nt r f d pp nt nt nd, th t 2Â F b. Th h ph rd l nd r. l X. TH H PH RD L ND R. L X. F r, Br n, nd t h. B th ttr h ph rd. n th l f p t r l l nd, t t d t, n n t n, nt r rl r th n th n r l t f th f th th r l, nd d r b t t f nn r r pr

More information

An idea how to solve some of the problems. diverges the same must hold for the original series. T 1 p T 1 p + 1 p 1 = 1. dt = lim

An idea how to solve some of the problems. diverges the same must hold for the original series. T 1 p T 1 p + 1 p 1 = 1. dt = lim An idea how to solve some of the problems 5.2-2. (a) Does not converge: By multiplying across we get Hence 2k 2k 2 /2 k 2k2 k 2 /2 k 2 /2 2k 2k 2 /2 k. As the series diverges the same must hold for the

More information

E[X n ]= dn dt n M X(t). ). What is the mgf? Solution. Found this the other day in the Kernel matching exercise: 1 M X (t) =

E[X n ]= dn dt n M X(t). ). What is the mgf? Solution. Found this the other day in the Kernel matching exercise: 1 M X (t) = Chapter 7 Generating functions Definition 7.. Let X be a random variable. The moment generating function is given by M X (t) =E[e tx ], provided that the expectation exists for t in some neighborhood of

More information

2.6 The optimum filtering solution is defined by the Wiener-Hopf equation

2.6 The optimum filtering solution is defined by the Wiener-Hopf equation .6 The optimum filtering solution is defined by the Wiener-opf equation w o p for which the minimum mean-square error equals J min σ d p w o () Combine Eqs. and () into a single relation: σ d p p 1 w o

More information

9740/01 October/November MATHEMATICS (H2) Paper 1 Suggested Solutions. (ii)

9740/01 October/November MATHEMATICS (H2) Paper 1 Suggested Solutions. (ii) GCE A Level October/November 9 Suggested Solutions Mathematics H (97/) version. MATHEMATICS (H) Paper Suggested Solutions. Topic: Matrices (i) Given that u n is a quadratic polynomial in n, Let u n an

More information

Econ 508B: Lecture 5

Econ 508B: Lecture 5 Econ 508B: Lecture 5 Expectation, MGF and CGF Hongyi Liu Washington University in St. Louis July 31, 2017 Hongyi Liu (Washington University in St. Louis) Math Camp 2017 Stats July 31, 2017 1 / 23 Outline

More information

Power Series Solutions to the Legendre Equation

Power Series Solutions to the Legendre Equation Department of Mathematics IIT Guwahati The Legendre equation The equation (1 x 2 )y 2xy + α(α + 1)y = 0, (1) where α is any real constant, is called Legendre s equation. When α Z +, the equation has polynomial

More information

Lecture 3 - Expectation, inequalities and laws of large numbers

Lecture 3 - Expectation, inequalities and laws of large numbers Lecture 3 - Expectation, inequalities and laws of large numbers Jan Bouda FI MU April 19, 2009 Jan Bouda (FI MU) Lecture 3 - Expectation, inequalities and laws of large numbersapril 19, 2009 1 / 67 Part

More information

ScienceDirect. ScienceDirec

ScienceDirect. ScienceDirec CRX_ / CR X_ / Q Q Q Q : R J : / // / J : / / N K * Jk k G U U U U N k U NC U : R k R J R H k - - - - - H - K: R - H - - V V V R - V V V - - L L H H - - C L H j q C L H j q k k k X k R k k X L k k k -

More information

Lecture 6: Gaussian Channels. Copyright G. Caire (Sample Lectures) 157

Lecture 6: Gaussian Channels. Copyright G. Caire (Sample Lectures) 157 Lecture 6: Gaussian Channels Copyright G. Caire (Sample Lectures) 157 Differential entropy (1) Definition 18. The (joint) differential entropy of a continuous random vector X n p X n(x) over R is: Z h(x

More information

Section 27. The Central Limit Theorem. Po-Ning Chen, Professor. Institute of Communications Engineering. National Chiao Tung University

Section 27. The Central Limit Theorem. Po-Ning Chen, Professor. Institute of Communications Engineering. National Chiao Tung University Section 27 The Central Limit Theorem Po-Ning Chen, Professor Institute of Communications Engineering National Chiao Tung University Hsin Chu, Taiwan 3000, R.O.C. Identically distributed summands 27- Central

More information

S tu d y P la n n e d Leader9s Expulsion Protested

S tu d y P la n n e d Leader9s Expulsion Protested x b 3; 5: D 8 G b 8 0 N U N V R Y 0< 25 965 G 9 x G O k K O N O R N N b N b U x k b b R RRN k V q U q 24 N x U b U 948 Rb 953 b b 25 D D b D b q b N b 954 U '-' jj X '?#»» j k 9 Kj x b j b U " ' b - R

More information

4 Moment generating functions

4 Moment generating functions 4 Moment generating functions Moment generating functions (mgf) are a very powerful computational tool. They make certain computations much shorter. However, they are only a computational tool. The mgf

More information

LOWELL WEEKLY JOURNAL.

LOWELL WEEKLY JOURNAL. Y k p p Y < 5 # X < k < kk

More information

Math Bootcamp 2012 Miscellaneous

Math Bootcamp 2012 Miscellaneous Math Bootcamp 202 Miscellaneous Factorial, combination and permutation The factorial of a positive integer n denoted by n!, is the product of all positive integers less than or equal to n. Define 0! =.

More information

CS5314 Randomized Algorithms. Lecture 18: Probabilistic Method (De-randomization, Sample-and-Modify)

CS5314 Randomized Algorithms. Lecture 18: Probabilistic Method (De-randomization, Sample-and-Modify) CS5314 Randomized Algorithms Lecture 18: Probabilistic Method (De-randomization, Sample-and-Modify) 1 Introduce two topics: De-randomize by conditional expectation provides a deterministic way to construct

More information

ECONOMICS 207 SPRING 2006 LABORATORY EXERCISE 5 KEY. 8 = 10(5x 2) = 9(3x + 8), x 50x 20 = 27x x = 92 x = 4. 8x 2 22x + 15 = 0 (2x 3)(4x 5) = 0

ECONOMICS 207 SPRING 2006 LABORATORY EXERCISE 5 KEY. 8 = 10(5x 2) = 9(3x + 8), x 50x 20 = 27x x = 92 x = 4. 8x 2 22x + 15 = 0 (2x 3)(4x 5) = 0 ECONOMICS 07 SPRING 006 LABORATORY EXERCISE 5 KEY Problem. Solve the following equations for x. a 5x 3x + 8 = 9 0 5x 3x + 8 9 8 = 0(5x ) = 9(3x + 8), x 0 3 50x 0 = 7x + 7 3x = 9 x = 4 b 8x x + 5 = 0 8x

More information

14 EE 2402 Engineering Mathematics III Solutions to Tutorial 3 1. For n =0; 1; 2; 3; 4; 5 verify that P n (x) is a solution of Legendre's equation wit

14 EE 2402 Engineering Mathematics III Solutions to Tutorial 3 1. For n =0; 1; 2; 3; 4; 5 verify that P n (x) is a solution of Legendre's equation wit EE 0 Engineering Mathematics III Solutions to Tutorial. For n =0; ; ; ; ; verify that P n (x) is a solution of Legendre's equation with ff = n. Solution: Recall the Legendre's equation from your text or

More information

NPDES Small MS4 General Permit (4RR040000) Annual Reporting Form. Title: Public Works Director. County: Crawford Address:

NPDES Small MS4 General Permit (4RR040000) Annual Reporting Form. Title: Public Works Director. County: Crawford  Address: ADQ NPDS Smll MS4 enerl Permi (4RR040000) Annl Rerin rm ARKANSAS Dermen nvirnmenl Qliy nin r mlein hi rm: ARR040000 reqire h hi rm be ed when bmiin nnl rer Y my reqe rvl e yr wn rerin rm Annl Rer re de

More information

1 Series Solutions Near Regular Singular Points

1 Series Solutions Near Regular Singular Points 1 Series Solutions Near Regular Singular Points All of the work here will be directed toward finding series solutions of a second order linear homogeneous ordinary differential equation: P xy + Qxy + Rxy

More information

if-.- starts, gtocilingsyfa., la Set.- TO LET. Valuable Real Estate for Sale! THE FOLLOWING ROOMS AXD OF.

if-.- starts, gtocilingsyfa., la Set.- TO LET. Valuable Real Estate for Sale! THE FOLLOWING ROOMS AXD OF. ER DERER bb R P b 2 p g p pp pbp pg p p pg bg Fg bb bp g b q 0 b p p b g $ bb bb 0 ( p ( bq p E Pb D b g g bbb q (q ( p q p q p q p p b pb pky ER PR FK P GE YD F RRD bg p g b gg b g g b g b b g b p p p

More information

[Read Ch. 5] [Recommended exercises: 5.2, 5.3, 5.4]

[Read Ch. 5] [Recommended exercises: 5.2, 5.3, 5.4] Evaluating Hypotheses [Read Ch. 5] [Recommended exercises: 5.2, 5.3, 5.4] Sample error, true error Condence intervals for observed hypothesis error Estimators Binomial distribution, Normal distribution,

More information

700 STATEMENT OF ECONOMIC

700 STATEMENT OF ECONOMIC R RM EME EM ERE H E H E HE E HE Y ERK HE Y P PRE MM 8 PUB UME ER PE Pee e k. ek, ME ER ( ) R) e -. ffe, ge, u ge e ( ue ) -- - k, B, e e,, f be Yu P eu RE) / k U -. f fg f ue, be he. ( ue ) ge: P:. Ju

More information

A = A U. U [n] P(A U ). n 1. 2 k(n k). k. k=1

A = A U. U [n] P(A U ). n 1. 2 k(n k). k. k=1 Lecture I jacques@ucsd.edu Notation: Throughout, P denotes probability and E denotes expectation. Denote (X) (r) = X(X 1)... (X r + 1) and let G n,p denote the Erdős-Rényi model of random graphs. 10 Random

More information

MAHALAKSHMI ENGINEERING COLLEGE-TRICHY

MAHALAKSHMI ENGINEERING COLLEGE-TRICHY DIGITAL SIGNAL PROCESSING DEPT./SEM.: ECE&EEE /V DISCRETE FOURIER TRANFORM AND FFT PART-A 1. Define DFT of a discrete time sequence? AUC MAY 06 The DFT is used to convert a finite discrete time sequence

More information

Progress, tbe Universal LaW of f'laiare; Tbodgbt. tbe 3olVer)t of fier Problems. C H IC A G O. J U N E

Progress, tbe Universal LaW of f'laiare; Tbodgbt. tbe 3olVer)t of fier Problems. C H IC A G O. J U N E 4 '; ) 6 89 80 pp p p p p ( p ) - p - p - p p p j p p p p - p- q ( p - p p' p ( p ) ) p p p p- p ; R : pp x ; p p ; p p - : p pp p -------- «( 7 p p! ^(/ -) p x- p- p p p p 2p p xp p : / xp - p q p x p

More information

Convergence in Distribution

Convergence in Distribution Convergence in Distribution Undergraduate version of central limit theorem: if X 1,..., X n are iid from a population with mean µ and standard deviation σ then n 1/2 ( X µ)/σ has approximately a normal

More information

Additional Practice Lessons 2.02 and 2.03

Additional Practice Lessons 2.02 and 2.03 Additional Practice Lessons 2.02 and 2.03 1. There are two numbers n that satisfy the following equations. Find both numbers. a. n(n 1) 306 b. n(n 1) 462 c. (n 1)(n) 182 2. The following function is defined

More information

UP TUB G. R. & I. Wo took tho train at EALERS ID Uragi.PatentKtdloinei.Psrlumtry

UP TUB G. R. & I. Wo took tho train at EALERS ID Uragi.PatentKtdloinei.Psrlumtry LLL NL G B- L - 60 VL V LLL GN NY Y 3 NB NY BL VY LLL Y- NNG -- K G B F BN: F x «5 $00 F VN L q L B K B B- - 3 6 L» q $00 $300 $00 $00 00 F q 600 00-00 900 L 500 00 500 000 5 0 BK Nx 00 500 50 3000 000

More information

AT AT. - bbf'rtistr. Commercial IS. parv N t r;prt';mi. l.i'ie. 1 'Ji r. Uu.rier t otunm..., lliiisl tttmjn..., al BUILDER, Steam Boilers, Furnaces,

AT AT. - bbf'rtistr. Commercial IS. parv N t r;prt';mi. l.i'ie. 1 'Ji r. Uu.rier t otunm..., lliiisl tttmjn..., al BUILDER, Steam Boilers, Furnaces, P??? 9 P P bb B PB 7 N N p b p N P p? ( ) ) ( $ ( p P DRR ( ( ( 6 9 D p x p x p p x p D g Q p? p g F g p p p PF Y b Fb b p N N ND PR N ( p) RN b N N DDN x p p p R p p ( B PP q g B( D G ( F N (D p b b NYR

More information

On corrections of classical multivariate tests for high-dimensional data

On corrections of classical multivariate tests for high-dimensional data On corrections of classical multivariate tests for high-dimensional data Jian-feng Yao with Zhidong Bai, Dandan Jiang, Shurong Zheng Overview Introduction High-dimensional data and new challenge in statistics

More information

:,,.. ;,..,.,. 90 :.. :, , «-»,, -. : -,,, -, -., ,, -, -. - «-»:,,, ,.,.

:,,.. ;,..,.,. 90 :.. :, , «-»,, -. : -,,, -, -., ,, -, -. - «-»:,,, ,.,. .,.,. 2015 1 614.8 68.9 90 :,,.. ;,. 90.,.,. :.. :, 2015. 164. - - 280700, «-»,, -. : -,,, -, -.,. -. -. -,, -, -. - «-»:,,, -. 614.8 68.9.,.,., 2015, 2015 2 ... 5... 7 1.... 7 1.1.... 7 1.2.... 9 1.3....

More information

Solid Thermodynamics (1)

Solid Thermodynamics (1) Solid Thermodynamics (1) Class notes based on MIT OCW by KAN K.A.Nelson and MB M.Bawendi Statistical Mechanics 2 1. Mathematics 1.1. Permutation: - Distinguishable balls (numbers on the surface of the

More information

Section 11.7 The Chain Rule

Section 11.7 The Chain Rule Section.7 The Chain Rule Composition of Functions There is another way of combining two functions to obtain a new function. For example, suppose that y = fu) = u and u = gx) = x 2 +. Since y is a function

More information

MATH 391 Test 1 Fall, (1) (12 points each)compute the general solution of each of the following differential equations: = 4x 2y.

MATH 391 Test 1 Fall, (1) (12 points each)compute the general solution of each of the following differential equations: = 4x 2y. MATH 391 Test 1 Fall, 2018 (1) (12 points each)compute the general solution of each of the following differential equations: (a) (b) x dy dx + xy = x2 + y. (x + y) dy dx = 4x 2y. (c) yy + (y ) 2 = 0 (y

More information