, Lecture 1
1 'Sample
=
space !
+A A exclusive
A =
0 A and are
disjoint/mutually
Au A = M
A <B
(FAOurthe
A
of B1
= is subect Boca
,
Al =
'Complement C A
A uB
=
'Union of A and B
An B = intersaction 1 and
of B
1) A n(Bvc) =
(A1B) v(Anz)
2) A v (B 1C) = (AUB) 1 /Arc)
3)(AnB) = Av B2
u) (AvB) =
AS 18
6) A (A(B) v
(A1B)
E
=
7) For partition Di ..... Ps and event A :
,
(A1Pi)
i. Classical definition
Requirement: all outcomes of the random experiment are
equally lively.
~(A) number of outsmes
probability of event A = P(A) = Total possible outcomes
(Where N(A) = # outcomes in ever Al
properties of this case :
· Ep(a) 1 1 for all events A
p(y) 0
=
adp(t) = 1
↑ /A VB) =
p(a) + P(B) if A , B are
disjoint
, ii. Empirical definitingcy probability
↓ Not all random experiments have equally likely outcomes
.
Requirement : the random experiment is
independently and identically
repeat able .
p : in a trails &
1 A) is the number
af
trails where A occurs
lim
P(A) =
1 1 = a constant
iii Subjective definition of probability
↑ (A)
is a
subjective believe in the occurance of A . It can
be used all random the problem is it's subjective
for experiments , ,
people would come up with different probabilities
General definition of Kolmogorov :
A Xioms
P(a) o
P(1) 1 =
P(A v B) = p(A) +
P(B) if they are disjoin
1 'Sample
=
space !
+A A exclusive
A =
0 A and are
disjoint/mutually
Au A = M
A <B
(FAOurthe
A
of B1
= is subect Boca
,
Al =
'Complement C A
A uB
=
'Union of A and B
An B = intersaction 1 and
of B
1) A n(Bvc) =
(A1B) v(Anz)
2) A v (B 1C) = (AUB) 1 /Arc)
3)(AnB) = Av B2
u) (AvB) =
AS 18
6) A (A(B) v
(A1B)
E
=
7) For partition Di ..... Ps and event A :
,
(A1Pi)
i. Classical definition
Requirement: all outcomes of the random experiment are
equally lively.
~(A) number of outsmes
probability of event A = P(A) = Total possible outcomes
(Where N(A) = # outcomes in ever Al
properties of this case :
· Ep(a) 1 1 for all events A
p(y) 0
=
adp(t) = 1
↑ /A VB) =
p(a) + P(B) if A , B are
disjoint
, ii. Empirical definitingcy probability
↓ Not all random experiments have equally likely outcomes
.
Requirement : the random experiment is
independently and identically
repeat able .
p : in a trails &
1 A) is the number
af
trails where A occurs
lim
P(A) =
1 1 = a constant
iii Subjective definition of probability
↑ (A)
is a
subjective believe in the occurance of A . It can
be used all random the problem is it's subjective
for experiments , ,
people would come up with different probabilities
General definition of Kolmogorov :
A Xioms
P(a) o
P(1) 1 =
P(A v B) = p(A) +
P(B) if they are disjoin
