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Co~bj~~oricj
(The
Ex:
A
≤ycietr
o
Co~sec
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of
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The
pc~ssbIc
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A
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com~un;~/,~
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i
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er
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be
e*-~c1fr 3 cL/dreg,
one c@ Iier cb/drtpi
a~≤~
nicr/Aer.~ áq~ h/er
choices
cif
A: We g.~jfl denc4e
~
hicdj~~
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caNs;sJ3 of
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her
avid
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4,
S
(io,ñ
(io,a) cio,3~)
nct~.,
di’ffec~jj
see
lhcif
there
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T1q5
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there ~ce vfl chokes 4r
c~
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{irsI ekmen~ crC the 1q,r and
these there ar’€ n c&oices ‘Rsr
element,
or-detect
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mn
there
pairs.
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of
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or
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at
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11,15
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1205≤;b/e
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This should be 10! 20! because there are 10! ways to permute the grads and then 20!
ways to permute the undergrads. The result follows from the basic principle of
couting.
2
Z
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res cc /L5
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the order
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kyvjct
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13
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~ tt’ie nc≤i4
vacsH,j
A.
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are
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posss4/e
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b~.J
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possi~b/e
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y.’ 6 34)!
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cci
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cr-cnn
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are
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or
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T~j5
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4;t~eted
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e
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order
c~v7
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is t~t~ sef
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I
(~/
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a;ffer~-t
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&
c~
experivfr?e~~r/
Iihi2j~
hor59ç
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the
ch;/~,
the
I~
eY/2&rflltP±
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in
L~ctv;kty
~
kocse
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p~ Yi~]/O~ns
1,2,
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pecv~’iud~}Yons
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S
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7/
eve~r/
ek~2e~-/3,
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C)
Er:
Coetirirls
exper;me~i
I”iff/n9.
-Lice1 +Lqe,~ 5:~/-?H, H7~
~1 I rMeqng t~ ‘flrrj ‘o$y
the Ste c~iJ
rest~, /~1ecJ 1~
11w evev,+ +hq~ cri
4t≤secl i~ ~$#,i4r,
The
ti~~#
3
t~e
C)
~iLt’~
ctre
the no4.~l;~.
se4s.
Let
Ekcln?p/e..
yOt~t
A
a
or
jn
os~
‘Ae~cJ~
yn4
resw/lr
,~
r-rJ,
wift
uS/n3
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Ierniinoioyy
A, f~
be
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be
tae4Zij
qs56c#kd
evenu/s.
A ~
rerw/h In heøds
*?,e
Ukflhc~,i
t~.
‘ñj, ~here
‘~eqds~ cintl
‘fl’rst
eve4 frs~jf 4h€ (‘rs’t
i3
the
Av@
Coin
‘rpj.
e-~-~
4he
L.’..-as
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‘the
/
71+,
~
A
ovid
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see eric4
The
o4~
tke..s
Av)3~LWM, H-r,rrj.
IlnO
ID
fliT
a~
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f/IC
5
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A ~J
/
II
co~pItnie~ of
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I
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A
(vl
A
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q~
I~4~i4~ve5
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c~
)
~(oc≤iI~
hectds)
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occ~r
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I
of ~n eve~±
pro
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cq~
be
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ref2~ci7’ ±1~e
occ~(ri~
a-c
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a
Tkecc
~Cr co~v11
ace
t~Is
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o~
reQgo~q~/e Je~~1~
These
~;/l
be
6e
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~
gkould eA-pec~
o~ probabG~
it gq~isTy,
~
c~//eJ
1
1:
2;
F1,
+he~
Node:
UUe
F, E~
A’
2
s/vP1
1P(F~).
ace
Or
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ny//
is
c~1lecf
the
evn~~
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eve~L€
I t~ece
~
Jelervv~ie
tiiese
±~ie
czY,ovnS.
qki
e~en~E
or
Ex:
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pco0l:
Let F, S ~1d E~, L3)
i~ Ks)z {P(O~ = LrI
+
:tTh
J
E~:
I
I~r
For
/fre5
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/
1 hr~
cuJco~es:
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/P(~I)t ‘kr)
1= ft~)-~ /PtUE~
r
~;
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t)P~5)r /PWE~)r ~F~)z
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=7 /P(E,)z/P4Fa)Z,,~/Tf~)
let A~z ~I1,
qre
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C
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j•
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ff(J1,2,~j)~ F(OAL) ‘Zfl~)
r
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L.
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c\
/
•
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;
--
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)
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ir)
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ci
coin
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If ECF, fke~ ~R’E)~F(~).
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TA~~ /~(F) P~ UA~)r~~)4qM2)
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~
Ly:
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ro/liy
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Propo~;4~o~9:
d~e3
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Q(A)4 ll(~)
1R7An~.
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=
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(P(A) /p64n8) (~ fl
Tk~~ fl)(A u3)~ ~(Al8) +4R7ip~c)±
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k~5
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Tk~5
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cohs;Jec
ny~ber
~vfn~
Let
be
QvI~
/€~
N<E)
Le~ F be
o~
o~I
Ez
E
o~
Ihe
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gec~~, aic,
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ivi F,
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in
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roiled +~ce.
i≤
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7
is
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eve~t
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Cc~ero~
Mixes
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5
o~
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L
1.
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II
b/ctck
4~~k
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reaches
ba/Is,
1~ /OrobQb?/4
h/~ck~
A: Tkece
coufj
‘S
a~(~
c~aicovne~~
Ex: A 60~J
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1.
The proof of this involves finding the moment generating
function and then showing that it converges the the MGF
of a standard normal.