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Unformatted text preview: aauemi
{KW-=0: 0.3
FLXEL) 1.10.2.—
W‘: PU=8)-=—=P
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o‘B+o.L+-i>+3p ==~l
:7 P: 9......5— :. 042.9"
L1 ... D‘PCX:&)-}- ; ~P£Xul>+L.PCX=3-> +3.PC‘K'=3) = 035+ 0M -+ 0-373"
= LD75’ Nah. 4% Eth is V1042 kw 01.5%. pmblfimz—
PCH)=P , PLTD= PP-
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has 0:.ch Mtg ~ ”NJ 5:» 75415 Ct?“ occm hung, m 4-14.21
acoltuwma swmw (hf fly); on?
X W Pwmb. 1.43 2- H, H (P f“ 1- "T, T Q- P) 3 H: T; H 1-0—19) 3 H )T; T— ECI—P)L 5 T: HLE‘ (PP) P1” 3 T: HM PUFF)?" PLX:;): P’C‘iH) H})+ P({T}TB)
=~ F1+ (VF);
g {Fa—l #2.? +p’” PLX=3>= KEHITJHE)+F(iH;T;TE)+P(i—r;HJH3>+P<1TEHJTE)
-=- FLU—PH ;>(a-—P)“+ F‘Ct-f) + PUFF)”
==— QFCW) +P<t—-P)L]
=— all Fl’P3+ PEFLPWP]
= .2 ( P— F“) Random Vatwtxhuew 11 4) ELK] = E ( I: ) pk(1 — p)“‘kk Note it = 3 term does not
k=fl contribute to sum.
11. Z :kr—(nfl _ k)!p"‘(1 _ flunk i=1
_ (fl. _ 1)'k—1n—k r _
_ up :1——_(k—1]I(n—k)'p 1(1— p) letk _Ic—1
_ “—1 (n — 1)! k’ n—l—ia’
— HP a; m? (1—?) sum of Binomial probe with parameter n — 1 and p
= up a! i flu
Ein] = Z flkflmpk (1 — p)“"‘ cancelling I: and letting ic’ = is: — 1 “E1 51*]. I ‘
:PZ(k’+1)( k; )P"(1-p)”'1"‘ H=D II
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with parameters in — 1 and 11 WW -1)p+1} Hi: = 5W] —5[X]2 = ”PH” —1)P‘+1“—”P} = ”PU -P) 5) 5X: m(#(_1)) __ m1 m
I] j; 1 1 a: rim—[1 $d$:lfl$1 am
1 W .1:
fl) £[X] = [mifil + mad: +1: «(1 + I“)d$
Consider the latter term:
If m _ 1 3 "' __ 111(1 + y)
In 'rr(l + mfidm 2w 111(1 +2: )5; _... 2n —+ no 3) a) Net reward Y = 1::le2 +bX—nd, where X is a. binomial RV E[Y] = £151le + bE[X] — :16
= «(EEIXI + Var [X]] + bE[X] — nd
= quip: + npq) + Imp — nd b)}’=n’" = U+L).€—s£
5[Nu: Mail: 2;“) EENM: ’Wt/u, ,]
{an Problem lfl Gt) 0 J 1&9-
ati>= .l--C1:-~l.,)) mix-Eb 5)
Lot 701(19195 Ham-r flan-$11? qun¢£:r’m 51 fiNaAMAé 593/. w:‘% men/u “at!
firming. 0-5: M ffxbc) dx + I 392(1) d1. = I
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)1 jfx(3rv)obfi L'- J; “”00 a mfg 1%,“ =7 Mel-GUEM' = /Ul ...
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- Spring '08
- GELFAND
- Trigraph, LOU EEK, surn cf Binomial, Rawaiam Var ithg, +an mpecmafi mméw
-
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