of 7 Measure

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

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←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¥

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= o.o ,

I g¥ =p .10

Rts X. X.,

.. .Xn af

I --t¥xi Var =Vardi

n

Pr - E I ? e) s VIDER

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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