STATISTICS
Least Upser Bound
(ALso called SUPREMU M)
IE s the lcast Value o all the hper bounds
particular Set 2n ts omain.
EEXAMPLE
XAMP Consider a set A=(0,2) and, ts domainn
R be
wouldher x22.o)7 bef
bound sce o
the seE A
22,)
ohe Least
Now
upe
theb0und/
leas, 34premum
uhher boumd=2 JoT setA
hor set A=(0,2)
2
Gqre atest Lower Bouno
Also callel IN FIMU M
94
JE sis thegeatest
9E value a l l lower bounds oh a a parti-
partl-
the
eular Set On ts
its domatn.
E AMPLPS
EXAMPLE Consider a set A=, ano its domaln
the set A RHereore
wOuld C,
Loyer boundd set
Noo the A
he greatest lower bound jor set A p
enera Jerms or Probabll2tu
2, SAMPLE SPACE he set oh all bossible outcomes
as o
OUm e v e n S nouon as ts
SAMPLE S PAC E
Ang gubsef samble sbace is known as a n
the
UNI oN Vheunio amy two events.s consisei
ents that are clther
A
A o B , ghese A, and B are the events o which
0%2
Unio n Aouwnd E 9 ,
Kee A={a} And B AUB=fa, b}
-UNIVERSAL SET
SET B
9ET A
UNION,OF
A and B
, 3,INTERS ECTION he intersecfion any,
evenes A amd consis =ng
even&s which 0nly have Occurred in A B bEtR.
the Sets
UNIVERSAL SET
-sET B
SET A
INTERSECTION
OF A & BB
MUTUALLY ExCLUsIVEJuwo eventS A and B,
are saidl to be, mutualy
ecclusive when 6oth 0amnot Occur *Multaneousl4
olnull seE) o
Sntersectiom both 3hould P nul set).
et AB nd B 6 ecclusivel
AdB
AnB Hence, they are mutually
5 COMPLEMENT COnsists
he com6emenG.6
o
am event ihS
aLl other outcomes which
re mot 2n Ao
-UNIVERSAL SETC
lco AC=1-A
-sETA
COMPLEMENT OF
SET A
6. 3 0BSET)orang2 evemtEs A
the o udcomes
amd
areas
aa A
then Uwe B a
that D Subset o A
Rebresemted as BCA
7 E g UAL OR IDENTICAL SETS Ator
andany 2 se
sets
s
A B OR A amol g
ACB
are
and CAYWeical sets
UNIVERSAL SET
SET A
SET B Yenn oiagram
3howiHg
SET BCSETA
Least Upser Bound
(ALso called SUPREMU M)
IE s the lcast Value o all the hper bounds
particular Set 2n ts omain.
EEXAMPLE
XAMP Consider a set A=(0,2) and, ts domainn
R be
wouldher x22.o)7 bef
bound sce o
the seE A
22,)
ohe Least
Now
upe
theb0und/
leas, 34premum
uhher boumd=2 JoT setA
hor set A=(0,2)
2
Gqre atest Lower Bouno
Also callel IN FIMU M
94
JE sis thegeatest
9E value a l l lower bounds oh a a parti-
partl-
the
eular Set On ts
its domatn.
E AMPLPS
EXAMPLE Consider a set A=, ano its domaln
the set A RHereore
wOuld C,
Loyer boundd set
Noo the A
he greatest lower bound jor set A p
enera Jerms or Probabll2tu
2, SAMPLE SPACE he set oh all bossible outcomes
as o
OUm e v e n S nouon as ts
SAMPLE S PAC E
Ang gubsef samble sbace is known as a n
the
UNI oN Vheunio amy two events.s consisei
ents that are clther
A
A o B , ghese A, and B are the events o which
0%2
Unio n Aouwnd E 9 ,
Kee A={a} And B AUB=fa, b}
-UNIVERSAL SET
SET B
9ET A
UNION,OF
A and B
, 3,INTERS ECTION he intersecfion any,
evenes A amd consis =ng
even&s which 0nly have Occurred in A B bEtR.
the Sets
UNIVERSAL SET
-sET B
SET A
INTERSECTION
OF A & BB
MUTUALLY ExCLUsIVEJuwo eventS A and B,
are saidl to be, mutualy
ecclusive when 6oth 0amnot Occur *Multaneousl4
olnull seE) o
Sntersectiom both 3hould P nul set).
et AB nd B 6 ecclusivel
AdB
AnB Hence, they are mutually
5 COMPLEMENT COnsists
he com6emenG.6
o
am event ihS
aLl other outcomes which
re mot 2n Ao
-UNIVERSAL SETC
lco AC=1-A
-sETA
COMPLEMENT OF
SET A
6. 3 0BSET)orang2 evemtEs A
the o udcomes
amd
areas
aa A
then Uwe B a
that D Subset o A
Rebresemted as BCA
7 E g UAL OR IDENTICAL SETS Ator
andany 2 se
sets
s
A B OR A amol g
ACB
are
and CAYWeical sets
UNIVERSAL SET
SET A
SET B Yenn oiagram
3howiHg
SET BCSETA
