, Pumability
Event
-
:
Let I denote the sample space .
e contains the set all outcomes of the random
of
.
experiment
: 2 =
<H ,
+ 3 7
2 = 91 ,
2
, 3
, 4 , 5, 63
2 =
(H , +H + T - . 3
, ,
-
-
C = [0 , 1]
# -Exeld: -
Let is be a collection of subsets .
2
of
le
say
B is
-field
a
if
i) PEB (B is
non-empty)
2) It CEB ,
CEB (B is closed under complements)
Y
complement of .
C
set C --
3)
If sequence of
the is in
a
B
CB i closed under countable union)
E e is the sample
space s-50
:
23 trival
2 =
(H , + ] ,
8-algebra
e <H3 5th3
Ey , , ,
, CeB ! peB ap" etB
= .
* (c . . . 7 B
=i
*
(G( - -
3 B ↑GEB ??
i=1
CitBaCieB ,
i = 1, 2 ,
- - -
-E
~
[ eB
= (4 t B
-B
En Let I be sample and Cl be
space
: a a
.
subset
8: B =
50 ,
2, C , C'] is a
-field .
Probability
# : (Aniomatic definition of
probability
Let t be a
sample space and B
let be a
T-field on .
e
It be real-valued function
Let a
defined on
B .
IP : B- IR
, Then IP is IP the
three conditions :
a
probability if satisfier following
1) P(C) >Of CGB
2) P(e) =
1
3) 4and
If is
sequence sets in B and
of
a
(disjoint Sequence of sett) then
Cn1Cm =
0 f MFn ,
P(E(n) = P(n)
En : C =
(H +3 ,
P(EH3) =
E1 P((T3) =
E
verifying 1) p(t) =P(CH +)) z z 1
I
, = + =
the
defi 2) PP(CH3) PCGT3)
=
+30 ,
=
t 40
3) PCCAUST3) = 1 =
c + = P(SH3) + P(GT3)
Eac =
E ,
Th
,
TH
,
TTH, - - - -
S
1) IP(CH3) IP((TH3) +
+40 30
= = - - -
, ,
2) IP(e) = P((H3) + IP([TH3) +
IPCETTHGle----
- He
=
+
--
- :/
End
3)
,
Sth3h
ID(CHU/T3) =
eg = P(CH3)-(CTA))
Event
-
:
Let I denote the sample space .
e contains the set all outcomes of the random
of
.
experiment
: 2 =
<H ,
+ 3 7
2 = 91 ,
2
, 3
, 4 , 5, 63
2 =
(H , +H + T - . 3
, ,
-
-
C = [0 , 1]
# -Exeld: -
Let is be a collection of subsets .
2
of
le
say
B is
-field
a
if
i) PEB (B is
non-empty)
2) It CEB ,
CEB (B is closed under complements)
Y
complement of .
C
set C --
3)
If sequence of
the is in
a
B
CB i closed under countable union)
E e is the sample
space s-50
:
23 trival
2 =
(H , + ] ,
8-algebra
e <H3 5th3
Ey , , ,
, CeB ! peB ap" etB
= .
* (c . . . 7 B
=i
*
(G( - -
3 B ↑GEB ??
i=1
CitBaCieB ,
i = 1, 2 ,
- - -
-E
~
[ eB
= (4 t B
-B
En Let I be sample and Cl be
space
: a a
.
subset
8: B =
50 ,
2, C , C'] is a
-field .
Probability
# : (Aniomatic definition of
probability
Let t be a
sample space and B
let be a
T-field on .
e
It be real-valued function
Let a
defined on
B .
IP : B- IR
, Then IP is IP the
three conditions :
a
probability if satisfier following
1) P(C) >Of CGB
2) P(e) =
1
3) 4and
If is
sequence sets in B and
of
a
(disjoint Sequence of sett) then
Cn1Cm =
0 f MFn ,
P(E(n) = P(n)
En : C =
(H +3 ,
P(EH3) =
E1 P((T3) =
E
verifying 1) p(t) =P(CH +)) z z 1
I
, = + =
the
defi 2) PP(CH3) PCGT3)
=
+30 ,
=
t 40
3) PCCAUST3) = 1 =
c + = P(SH3) + P(GT3)
Eac =
E ,
Th
,
TH
,
TTH, - - - -
S
1) IP(CH3) IP((TH3) +
+40 30
= = - - -
, ,
2) IP(e) = P((H3) + IP([TH3) +
IPCETTHGle----
- He
=
+
--
- :/
End
3)
,
Sth3h
ID(CHU/T3) =
eg = P(CH3)-(CTA))
