rules
counting
chores h
:
1- K
.
2
Note 11
:
:
distinct inputs
every
bijection
has
image
between 2
bijection S and A
one-to-one
:
Cantor set :
onto
,
ways
* " 2*7
Lagrange
151
→
a
sets
outputs
f(x)≠ Hy )
≠y
and
text #g)
cardinality
e.
g.
IN & 2N
IN &
,
It , IN
49-1
& 2
IN /
is ≤
from 5
[0,1 ]
to
of each
segment
.
uncountable
↑
uncountable
Note 13
sample space
R
of
sample poms
random
experiment : draw sample of kekms from sets cardinality
≤
properties :O Pcw ] ≤1 from WER fon negativity )
,
=
n
-
PED =/
,
event
A
↓
PCB]
posterior probability of
probability
PCA ] : prior
Bayes
one
)
is subset of R
Note 14
PCA / B) =P [An B)
'
Ctota /
Rule :
of A,B≤r
A)
PCAIB ]
space, PCB ] -0
probability
Cdetn of conditional
probability )
PCBIA] PCA]
=
=
same
-
PCB ]
Probability Rule
P[ B) PLAN B ]tp( A- A B) PCBIAJP (A) + PIB / A- Jp (A) =P ( BIA]P[ A) 1- PCBIA ] a- HAD
Total
=
=
so
p[A / B) =P
-
A
panitioned
into
A
(union of subsets)
, ,
.
.
,
An
plan B) =P [A] PCB]
=
=P (A)✗ PCB]
PCB]
tf
subset 7- ≤
Bayes
'
{1
,
.
.
;n },
;
=
-
-
'
(
and Ai NA
;
VAN
=
A
given ,B≤ d)
PIA]
=
or
b- Bit { Ai A-; } PCB
,
PCBIA;] PCA ;] =p [ PIA;] PCA ;]
-
-
PCB]
W­
UAZU
PCB]
/It ≥2PI±A ]=I¥(A ;]
Rule from :P( Ai IB ]
,
independent
.
PLAID] PLANT
if :A=A
¥4
PCBIA ;] PCA;]
-
,
A. in
P[
Bn]
=
!IP(Bit
A ;] ≤
É PCA ?
,
it
-
ez )
∅ for all i=j (disjoint)
ᵈ
.
_
.
inverse
diision
.
ECD-0 ¥mprd
azlitazxtqxtao
Pci ) Eli )=r Eli )
;
Qcx):p CHECK)=
countable 5
subset of A
fond malt
)=%É%yg
B ECH-tx-e.lk
✗ =y
-
keep removing middle }
map
✗
pre image, (Ky) # ×) ftp.r-y
same
some
or
distinct
other roots
s ex
,
one-to-one
Onto
,
"
,
every eyas