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Fo DA.
Concentration
L 7°
of
Measure
praobablgd-pproxcorreet-CPAdunb.no- n function ( pdf ) f
IX.,
. . .Xn÷£I = I Et Xi
Pr x - Efee ] so
I ← I error probabilitytolerance at
Efi;failure
MasterlyRv
.X
(a) X Zo (b) Eff ] known
"
sdpiqsaya.EEE = a - Efx ] are ECPr [ X - Efe ] > e ] s are FEI
Et Efx ]
a¥¥iECD a
°ELN
E Cx ] - o . prfx .
. o ] + a. pIxTo
= o . ( I . s ) + a . d = a . d
Eft ]a-
= or
Pr ( x I 5) I⇐0.6
←Eto
E=3 .
>
a
a.
85Pr L* > ⇐D) E I = a .ie
-o
.
56.5Eat
qEs. ÷t
June expect rain of SLC
R .U
. R
ECR ] = 20mm
Prob Rain in June in SLC 250mm
PREK ? soon ] I E÷r?= =or4
Pr[R ? 10mm ] E = z
¥¥r¥-1 .
cheeh.bssheulnequalits-R.li.
x
⑨ EG ] (b) Var C x ]for ans E 70
' II :* ,"¥÷¥⇒ev:SGmm3om#↳ a
¥ . .
Rainfall Jon . in SLC
RU .R
E = 20mm Var CR] = 9mm '
90mm '
Pr [ R 250mm ) EPr ( R -Eat? z som )
I Pr[ IR- ECR ]/230mm]
± ↳4¥
" ± V%f# ÷.
= o.o ,
I g¥ =p .10
Rts X. X.,
.. .Xn af
I --t¥xi Var =Vardi
n
Pr - E I ? e) s VIDER
Varcx :]awe .
it.EE?c. e± or
prob . failure of
How mang samples ( is ) are needed
n =Varleyis
chernoff-Haeffdinglnequal.it#n Rts X.,X
. ,. . .
Xn Tid fE east ¥71 casecxis ④ Xi c- Cb't?.pk?jnII&...oo,E- exp
7E⇒n&_¥¥.men fix - E I ze]E2exp(ns.E.ee#cE2expf2jY)
Given i E,S
, D How many samples C n )
are needed
n= II info )
Roll Dice n - 120 times
Rt.
To # roll a 3⇐ '
ere ,
" o . ÷ . . .
f÷÷÷÷⇒,
I ?I -
- I .&x:
F- In 120
= PREZ 's ]EPrff-ECM.lzf-JE-t.EE,it
=hits- I
C - H I 2e×p(-Z)6=12= Zexpf -
F) so . 0026
caesuras .
s ' ¥i¥i÷÷. "
vortex ] = Er Io