Mathematical
Theory
t
Notation
Subscripts -
Contingency Table
EQU
value in table
>
-
specific at
position is
commen
total .
e for
g.
· > <
j total
colj
-
+
.
j2 >
average
-
Sigma Notation
no of terms
⑭
.
constant
E
· Qchanging
=
x + + +C
,
. .
n
2
stats
G-Standard deviation
Factorial Notation
0! =
1
n! =
n (n 1) (n 2) - -
...
(2) (1)
3! 3x2 x1 6 be diff
eg. arranged
in 6
ways
=
=
>
-
can
, Integration
Definite : W f()dx =
F(x)
Indefinite : (f() &x =
F(x) +
probabilities
0 (P(A)2)
sample Space - =
& 3 +
outcome set
containing elements (possible outcomes
=
exhaustive ?
Event : subset (f) of sample space
Mutually exclusive
>
events
-
·
of do not
outcomes events overlap
>
Mon-mutually exclusive
-
#
·
outcomes overlap
Independent Event
each unaffected
> outcome is
by the previous outcome
-
Dependent Event
, Terminology
·
statistical experiment
>
-
unpredictable result
·
sample space of X >
-
all possible outcomes of the event
Random variable (r U )
. .
>
-
numerical independent outcome
(unpredictable)
·
Intersection of events/sets (1) >
-
outcomes that occur in both events
(no muta
·
Union of events/sets (U) >
-
all possible outcomes in both events
.g
e .
if P(A) = x
Complement (A
·
or Al >
-
all elements not contained in the subset of the outcome set
P'(A)
-
not A
= I
=
complement
Exhaustive set (sum 1)
·
of the
-> all possible outcomes sample space of their probabilities =
Classical Probability
all
>
-
outcomes are
equally likely to occur in on event same
probability
Empirical Probability
>
-
probabilities determined by replication of actual
experiments
Subjective Probability
>
-
probabilities based on educated guesses
No Of outcomes in favour of event
P(A)
.
=
no . of outcomes of experiment
Mutually exch : PLAUB) =
P(A) + P(B)
Non-mutually excl: P(AUB) = P(A) + P(B) =
P(AB)
, Independent non-mutually exclusive :
P(A1B) =
P(A) P(B)
Conditional Probabilities :
the outcome of
> outcome of one event is affected by another event
-
ADATB)
PCAB)=
=
robability of even
Agea
event B
>
-
" Vice versa
Dependent non-mutually exclusive :
P(A 1B) = P(B) P(AIB)
Theory
t
Notation
Subscripts -
Contingency Table
EQU
value in table
>
-
specific at
position is
commen
total .
e for
g.
· > <
j total
colj
-
+
.
j2 >
average
-
Sigma Notation
no of terms
⑭
.
constant
E
· Qchanging
=
x + + +C
,
. .
n
2
stats
G-Standard deviation
Factorial Notation
0! =
1
n! =
n (n 1) (n 2) - -
...
(2) (1)
3! 3x2 x1 6 be diff
eg. arranged
in 6
ways
=
=
>
-
can
, Integration
Definite : W f()dx =
F(x)
Indefinite : (f() &x =
F(x) +
probabilities
0 (P(A)2)
sample Space - =
& 3 +
outcome set
containing elements (possible outcomes
=
exhaustive ?
Event : subset (f) of sample space
Mutually exclusive
>
events
-
·
of do not
outcomes events overlap
>
Mon-mutually exclusive
-
#
·
outcomes overlap
Independent Event
each unaffected
> outcome is
by the previous outcome
-
Dependent Event
, Terminology
·
statistical experiment
>
-
unpredictable result
·
sample space of X >
-
all possible outcomes of the event
Random variable (r U )
. .
>
-
numerical independent outcome
(unpredictable)
·
Intersection of events/sets (1) >
-
outcomes that occur in both events
(no muta
·
Union of events/sets (U) >
-
all possible outcomes in both events
.g
e .
if P(A) = x
Complement (A
·
or Al >
-
all elements not contained in the subset of the outcome set
P'(A)
-
not A
= I
=
complement
Exhaustive set (sum 1)
·
of the
-> all possible outcomes sample space of their probabilities =
Classical Probability
all
>
-
outcomes are
equally likely to occur in on event same
probability
Empirical Probability
>
-
probabilities determined by replication of actual
experiments
Subjective Probability
>
-
probabilities based on educated guesses
No Of outcomes in favour of event
P(A)
.
=
no . of outcomes of experiment
Mutually exch : PLAUB) =
P(A) + P(B)
Non-mutually excl: P(AUB) = P(A) + P(B) =
P(AB)
, Independent non-mutually exclusive :
P(A1B) =
P(A) P(B)
Conditional Probabilities :
the outcome of
> outcome of one event is affected by another event
-
ADATB)
PCAB)=
=
robability of even
Agea
event B
>
-
" Vice versa
Dependent non-mutually exclusive :
P(A 1B) = P(B) P(AIB)
