7 prfx Pi PJ i I i oprcx E nP Aside Var X l p Letz np is - - PDF document

SLIDE 1

Zoo

• f

r

v

s

Bernoulli p

7 f Bercp

has dish of

Z I

w prob p

O

l p

F 2

p

Van

2

p Tp

Binomial hip

Xv Binfn p

dit's in

n'iodintosses

eachw probpof coming

up H's

X

X

tXzt

Xn

Xi

Beep

Xi's

are mutuallyindep

X takes

valves

0 1,2

gh

prfx

i

7

Pi

PJ

• prcx

i

I E

nP

Aside

Var X

np

l p

Letz

is

a.ru

Vm X pVafXDtVafX

t tVaCXY

I

PrCZ

a

because

Xi's

are mutually

ac Rangek

indef

Cb F

Fx a

Pr Xia

monotone fr

from o to

1

Van X7y2

Von

Vanya

XRyan indep

Xdand42 areindep

SLIDE 2

Ex

sending

a

bit

string

• ver a

network

each

bit

corrupted independently

with prob p

corrupted bits

Bin nip

n

106

p

10

5

exp of

corrupted bits

O n oeylage

hp

cast

I

2

n

1

4

1

1

Prob ever.it many guen tiny interval

p

intervals ish events

indep

hp

events

t

n

Pr

X

• c p

e

I xtxf if very

tiny

EP

e Pn

tetra

a

e

Pr

XI

Y

p Ci p npci pjhnpe.PH

ripe

in

a re

Prats

2 pacep5 Ige

Xv Binh p

lem

PrCX

ik e

A HSN

hp

a

SLIDE 3

I

Poisson

N

Ztahes 9112

Pre

K

e

I

k

I EIPre

k

zE

e

ak

Korczak

k

ke

E

ke zK

Tieng

L

ko

k

Vonk

a

1

1

events happen at

1

theumt

rang Munthe

SLIDE 4

Conditional expectation of

X

given event A

F XIA

a PRIX

a

A

acRage

Law of

Total

Expectation

F

X

E Xl A

PRCA

tECxIA PrfA

Pf

Efx

Ergot PrY

ELN

LawgFalprob

a

µ j Pr X xlA Prm

tPrCX xfE PRIED