Polling + Auctions Anna Karlin Agenda idealized An application - - PowerPoint PPT Presentation

polling auctions
SMART_READER_LITE
LIVE PREVIEW

Polling + Auctions Anna Karlin Agenda idealized An application - - PowerPoint PPT Presentation

Polling + Auctions Anna Karlin Agenda idealized An application of The Central Limit Theorem Polling A glimpse of auction theory Magic mushrooms He were Yesterday, Oregonians are voting on whether to legalize the F therapeutic use


slide-1
SLIDE 1

Polling + Auctions

Anna Karlin

slide-2
SLIDE 2

Agenda

  • An application of The Central Limit Theorem – Polling
  • A glimpse of auction theory

idealized

slide-3
SLIDE 3

Magic mushrooms

Yesterday, Oregonians are voting on whether to legalize the therapeutic use of “magic mushrooms”. If you take a "heroic" dose, supposedly, “the ego dissolves and the user feels inseparable from the rest of the universe.”

He were

F

Poll

to determine fraction of population

that will

be voting

in favor

call up

a random sample

report

empirical Aachen

is this

goodestimate

how choose

n

slide-4
SLIDE 4

CLT à Polling on magic mushrooms

This

poll is accurate to within

2

19tinesortg20

chance

estimate

garbage

estimate

is within

2

  • f

the answer

Populationsize

N

p

the Aachen votingin favor

We don'tkno wp

far

in

1 to

n

pick uniformly random person to call

TN

X

1

votingin favor

O W

X

Xa

Xn

I

I

I

O

O I 1

h

500

Estivate

271

n

500 0542

EX

271

5

1

2

slide-5
SLIDE 5

gth.eu

EAD Van

What kind of riv

is Xi

F

a

Bernoulli

p

php

wimprobp

Bfenmmti.EE

TT.fyXi

ftp.pq

d Poisson

P PKP fI

t

X

ECI

Vm

empirical mean

a

rip hpap

b

p

pup LL

X Ya

gkn

I

TPH

va zx

are

independent

d

E

P

hate

i Id

Beep

Van ay

away'D

slide-6
SLIDE 6

The Central Limit Theorem

Consider i.i.d. (independent, identically distributed) random vars X1, X2, X3, … Where Xi has μ = E[Xi] and σ2 = Var[Xi] As n → ∞, Restated: As n → ∞,

Mn = 1 n

n

X

i=1

Xi → N ✓ µ, σ2 n ◆

Xn

standardize

do

O

I

EEEpa.FI

YefpiIfI

slide-7
SLIDE 7

By

at

Ht

g

agnnqyigasn

s

x.is

PrflT P

g

Lidocaine

i

n

T

iIoo

4Iding

fggqoghnemye.hn

niswifrI

Eksda

ITT

T

µ

n

D.tn

aagprfp

  • .o5

Ipog

m

a

CT

th

slide-8
SLIDE 8

c

I

Pr

LI pl

0.05

I

Nlp MIL

Prf

Is

5 panto

PII

v

is

N

N 0,1

INTEND

s

a

w

p

E

D

And ns.t

fpm edz

slide-9
SLIDE 9

And

h

Pr

I

0.02

Pr

2 ir

tPrfzs

  • .lrn

2PrT

rn

3

I

prczeo.ir

H

E

t

Es

i oICo.ir

  • _0

tan

543

  • .aaeoIG.ir

7

air

32.33

Toi.sofigin

n'Io ITs

slide-10
SLIDE 10

The Standard Normal CDF

ETH337 0.99

slide-11
SLIDE 11

pry 4

a

E

n

do not

knowp

Prf 14

a

prft4sb

L

Prf 14

c

slide-12
SLIDE 12

X

Berge

Xp

Beep

prcx.ie

Pr

X

  • XED

PrfXoa l XEO

slide-13
SLIDE 13

END PIC

Alex Tsun Joshua Fan