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): Now supposl that X, n ari undependent and e atugy Mi Lt)s exp {e;t? yor all i E { 1, ".n}.gor t ER ... a) show that for any t > 0 p (x> 8):Ple tX>est) < exp (o? t/2 -6t)· C. HINT: Uae Markov's inequality yor any hon · Kigatue pandom vari able Y, P(Ysa) 2E Let Š= ĥ E,Xi all し=/ thow that Män (t) Eexp that rince ine quality ): exp b) . Nete 2n2 (1) holde jor alul *0く? P (x >s)= min cxp (t'tp$}) 0く? Ming that, ehow 2 d). Uee parts C6) G Cc) to PCX >S) E exp ( show that PC Ăn >)Eexp 202 #INT: 9 ind the t>o that minmmizes eap coz4/2 -6t)

): Now supposl that X, n ari undependent and e atugy Mi Lt)s exp {e;t? yor all i E { 1, ".n}.gor t ER ... a) show that for any t > 0 p (x> 8):Ple tX>est) < exp (o? t/2 -6t)· C. HINT: Uae Markov's inequality yor any hon · Kigatue pandom vari able Y, P(Ysa) 2E Let Š= ĥ E,Xi all し=/ thow that Män (t) Eexp that rince ine quality ): exp b) . Nete 2n2 (1) holde jor alul *0く? P (x >s)= min cxp (t'tp$}) 0く? Ming that, ehow 2 d). Uee parts C6) G Cc) to PCX >S) E exp ( show that PC Ăn >)Eexp 202 #INT: 9 ind the t>o that minmmizes eap coz4/2 -6t)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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#oegy dling s une qu ality proudis an upper probakility that the sum 6 founde d in dipindent random vari ablis oleviatis prom its t orind on the expicted value mere Than a amount Ihe inec crt ain equality gener alized has qurther kein yor unboun ded random vari'akus and findr many applications in machine learnin g theary: In Ahis exercine, me ull Mo dirn proe d one - sudi d a Heagf aing's ine quality The tuo · si ded version can ar gue d ty symautry, uhid uili omit yor this be ine problem · iuppase x hae Moment Senerating Function Mx Ct)- Ee tu For simplicity ausume that EX=0 san dom vare able Auume that there exuts o> 0 uch that Mx (t) < exp fot? per all t ER.
Transcribed Image Text:#oegy dling s une qu ality proudis an upper probakility that the sum 6 founde d in dipindent random vari ablis oleviatis prom its t orind on the expicted value mere Than a amount Ihe inec crt ain equality gener alized has qurther kein yor unboun ded random vari'akus and findr many applications in machine learnin g theary: In Ahis exercine, me ull Mo dirn proe d one - sudi d a Heagf aing's ine quality The tuo · si ded version can ar gue d ty symautry, uhid uili omit yor this be ine problem · iuppase x hae Moment Senerating Function Mx Ct)- Ee tu For simplicity ausume that EX=0 san dom vare able Auume that there exuts o> 0 uch that Mx (t) < exp fot? per all t ER.
): Now suppse that X, . Xn ari independent and e atiugy Mi lt)s exp {e?? yer all i t { 1, .n} .gor i= ,... , h, from part [d) ... t > 0 a) show that for any P (x > 8).Ple txsest) < 2-8t). cxp co? t /2-6+) HINT: Mae Markors inequaluły yor any varu able Y, PCYsa) EY all t ER hon higatuve pandom thow that Mãn Ct) Eexp a b) . Nete that since ene quality ): exp i 2n2 (1) helda jou alu t>o, (こ,) i P Cx >S) ļ min exp (ot2-st) 0く? Ming that, show d). Uee parts C6) G cc) to P CX >8) Ź exp (- 202 show that PC Ăn >$)< #INT: I ind the t>o that e xp minmizes exp (o?t/2-St) c) E ). Uhen oi= 0, gor all (= 1,... , n, rom part (d) ノ con clu de that p ( Xm >s)s exr {-+
Transcribed Image Text:): Now suppse that X, . Xn ari independent and e atiugy Mi lt)s exp {e?? yer all i t { 1, .n} .gor i= ,... , h, from part [d) ... t > 0 a) show that for any P (x > 8).Ple txsest) < 2-8t). cxp co? t /2-6+) HINT: Mae Markors inequaluły yor any varu able Y, PCYsa) EY all t ER hon higatuve pandom thow that Mãn Ct) Eexp a b) . Nete that since ene quality ): exp i 2n2 (1) helda jou alu t>o, (こ,) i P Cx >S) ļ min exp (ot2-st) 0く? Ming that, show d). Uee parts C6) G cc) to P CX >8) Ź exp (- 202 show that PC Ăn >$)< #INT: I ind the t>o that e xp minmizes exp (o?t/2-St) c) E ). Uhen oi= 0, gor all (= 1,... , n, rom part (d) ノ con clu de that p ( Xm >s)s exr {-+
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