Tuesday, June 30, 2020

Mathematical Symbols - Statistics and Probability

Mathematical Symbols are very important to learn mathematics, on using symbols we can easily understand the concepts of topics.

Generally, Mathematical Symbols can be categorized on their importance in the following ways:

Mathematics symbols - Number

Mathematics symbols - Basic

Mathematics symbols - Algebraic

Mathematics symbols - Geometric

Mathematics symbols - Trigonometry

Mathematics symbols - Set Theory

Mathematics symbols - Statistics & Probability

Mathematics symbols - Calculus And Analysis

Mathematics symbols - Logical & Reasoning

Mathematics symbols - Roman

Mathematics symbols - Greek

Mathematics symbols - Miscellaneous

Now we shall learn /discuss seventh topic Mathematics symbols - Statistics and Probability on this post.

Mathematics symbols - Statistics and Probability

These are very important Basic Tools frequently used by us not only in statistics and Probability but also in Operation Research, Management as well as in other branches of applied mathematical sciences and engineering.

Table of important Mathematical Symbol of Probability and Statistics

S.N.

Symbol

Name of Symbol

Definition

Illustration

1

P(A)

Probability Function

Probability of any event A

P(A) = 0.2 or any number between 0 to 1

0 ≤ P (A ≤ 1

2

P(A) = 0

Complete Uncertainty

The event cannot happen

On tossing a coin we shall get prime number.

3

P(A) = 1

Complete certainty

The event will happen definitely

On tossing a die we shall get a number less than 7.

4

P (A ∩ B)

Probability of intersection of events

Probability of Event A and B

P (A ∩ B) = 0.5

5

P (A ⋃ B)

Probability of union of events

Probability of Event A or B

P (A⋃B) = 0.5

6

P (A / B)

Conditional Probability Function

Probability of Event A when B already occurred.

P (A / B) = 0.2 or any number between 0 to 1

7

P (B / A)

Conditional Probability Function

Probability of Event B when A already occurred.

P (B / A) = 0.6 or any number between 0 to 1

8

μ

Mean or population mean

Mean of population values

Mue = 10

9

f(t) or f(x)

pdf

Probability Density function

P (a ≤ t ≤ b) = ∫ f (t) dt, where t is any variable can be replaced by x or y etc.

10

F (t)

cdf

Cumulative distribution function

F(t) = P (T≤ t)

11

E (X)

Expectation Value

Expected value of any random variable x

E (X) = 10

12

E (X / Y)

Conditional Expectation Value

Conditional Expected value of any random variable X given Y

E (X / Y) = 3

13

E (Y/ X)

Conditional Expectation Value

Conditional Expected value of any random variable Y given X

E (Y / X) = 2

14

Sigma 2 (σ 2)

Var(X)

Variance of random variable x

Var(x) = 16

15

∑

Sigma (Capital)

Summation

Sum of all values in the range.

16

∑∑

Sigma (Capital) Sigma (Capital)

Double Summation

Sum of all values in the range.

17

Range

Range

Difference between maximum and minimum value

For series 2, 4, 6, 10, 10, 10, 20,40

Range= 40-2 = 38

18

MR

Mid-range

½(Maximum + Minimum )

For series 2, 4, 6, 10, 10, 10, 20,40

MR= ½(2 + 40) =21

19

Mo

Mode

Value that frequently occurs in data / population / series. Or

Maximum number of repetitions

For series 2, 4, 6, 10, 10, 10, 20,40

Mode = 10

20

X bar

Sample Mean / average / Arithmetic Mean

Sum of all observations / No. of observations

For series 2, 4, 6, 10, 10, 10, 20,40

Mean = 1/8 (2+4+6+10+10 +10+20+40)

21

Std(X) or

σ(x)

Standard deviation

Standard deviation of random variable x = square root of variance

For any observation, if Var(x) = 16 then

Std(X) = 4

22

Median

Median

Mid value of x

For series 2, 4, 6, 10, 10, 10, 20,40

Median = 10

23

cov (x, y)

Covariance

Covariance of any random variable x and y

cov(x, y) = 4

24

corr (x, y)

Correlation

Correlation of any random variable x and y

Corr (x, y) = 4.5

25

ρ(x, y)

Correlation

Correlation of any random variable x and y

ρ (x, y) = 4.5

26

Q

Quartile

% population are below this average on the basis of Q1, Q2, or Q3.

27

Q1

First Quartile / lower

25 % population are below this average or first quartile

28

Q2

Second Quartile / Median

50 % population are below this average



29

Q3

Third Quartile / Upper

25 % population are above this average or

75 % population are below this average

On having knowledge of the above Mathematical symbols of probability and statistics, we can easily enhance our subject ideas.

___________________________________________________________

Mathematical Symbols - Set Theory

Mathematical Symbols are very important to learn mathematics, on using symbols we can easily understand the concepts of topics.

Mathematical Symbols can be categorized on their importance in the following ways:

Mathematics symbols - Number

Mathematics symbols - Basic

Mathematics symbols - Algebraic

Mathematics symbols - Geometric

Mathematics symbols - Trigonometry

Mathematics symbols - Set Theory

Mathematics symbols - Statistics & Probability

Mathematics symbols - Calculus And Analysis

Mathematics symbols - Logical

Mathematics symbols - Roman

Mathematics symbols - Greek

Mathematics symbols - Miscellaneous

Now we shall learn /discuss Sixth topic Mathematics symbols - Set Theory on this post.

Mathematical symbols - Set Theory

These are very important Basic Tools frequently used by us in Particular topics of algebra like Sets and relations, Pure Algebra, Mathematical Logics as well as in other branches of applied mathematics and sciences.

Set can be written by capital alphabets like A, B, C, P, Q, X, Y, etc and it can be written in Curley Brackets.

S.N.

Symbol

Name of Symbol

Definition

Illustration

1

{ }

Set

A well-defined collection of objects / elements are known as a set.

A = {1,17,19,24},

B = {3, 7,19,24}, OR

C= Set of word MATHEMATICS

= {M, A, T, H, E, I, C, S}

2

A = B

equality

both sets have the same members (orders may be different)

A = {1,2,3,4}

and

B = {1,2,3,4}

3

A ∪ B

union

Those objects which belong to set A or set B.

If A = {1,17,19,24}, and

B = {3, 7,19,24}, then A ∪ B =

{1, 3, 7, 17, 19, 24}

4

A ∩ B

intersection

Those objects that belong to set A and set B both.

If A = {1,17,19,24}, and

B = {3, 7,19,24}, then A ∩ B = {19,24}

5

A ⊆ B

subset

A is a subset of B or set A is included in set B.

{1,2,3,4} ⊆ {1,2,3,4}

6

P ⊂ Q

proper subset or a strict subset

“P is a subset of Q, but Pis not equal to Q”.

{1,2, 4} ⊂  {1,2,3,4}

7

P ⊄ Q

not a subset

"The first (P) set is not a subset of another or second (Q ) set "

{1,2, 4} ⊄ {1,22, 44}

8

P ⊇ Q

superset

P is a superset of Q or set P includes set Q

{1,14,28} ⊇ {1,14}

9

P ⊅ Q

not a superset

set P is not a superset of set Q

{19,14,208} ⊅ {19,23}

10

power set

All subsets of any set like A

11

P (A)

power set

All subsets of any set like A

12

complement

All the objects that do not belong to given set A

13

complement

All the objects that do not belong to given set A

14

A – B

Set A-minus Set B

Or

relative complement

Objects that belong to set A and but not to set B

If A = {1,2,3,4} and

B = {1, 2, 5, 7}

then

A-B = {3, 4}

15

A / B

Set A minus Set B

or

relative complement

Objects that belong to set A and but not to set B

If A = {1,2,3,4} and

B = {1, 2, 5, 7}

then

A-B = {3, 4}

16

B – A

Set B minus Set A

Or

relative complement

Objects that belong to set B and but not to set A

If A = {1,2,3,4} and

B = {1, 2, 5, 7}

then

B- A = {5, 7}

17

B / A

Set B minus Set A

or

relative complement

Objects that belong to set B and but not to set A

If A = {1,2,3,4} and

B = {1, 2, 5, 7}

then

B- A = {5, 7}

18

a ∈ A

belongs to

OR

elements of

Element is member of a given set

If A = {1,2,3,4}

then

1 ∈ A, 2 ∈ A,

3 ∈ A, 4 ∈ A

19

a ∉ A

Not belongs to OR

not element of

Element is NOT a member of given set

If A = {1,2,3,4}

then

5 ∉ A

20

A ∆ B

Symmetric difference of sets

Set of all those elements that belong to A or B but not to their intersection.

(A ∪ B) – (A ∩ B)

OR

(A - B) ∪ (B - A)

If A = {1,2,3,4}

and

B = {1, 2, 5, 7}

then

A ∆ B = {3,4,5,7}

21

A ⊖ B

Symmetric difference of sets

Set of all those elements that belong to A or B but not to their intersection.

(A ∪ B) – (A ∩ B)

OR

(A - B) ∪ (B - A)

If A = {1,2,3,4}

and

B = {1, 2, 5, 7}

then

A ⊖ B = {3,4,5,7}



22

(x, y)

Ordered Pair of x and y

Set of two elements whose order is fixed.

23

A × B

Cartesian Product

it is a set of all possible ordered pairs from A and B

24

B × A

Cartesian Product

Set of all ordered pairs from B and A

25

n (A)

The cardinality of set A

The total number of elements of the set A

A = {1, 2,3,9,14},

n(A) =5

26

|A|

The cardinality of set A

The total number of elements of the set A

A = {1, 2,3,9,14}, |A|=5

27

(Phi)
Empty Set

The set having No elements.

28

(Zeta)
Universal Set

Superset of all sets

On having knowledge of the above Mathematics symbols - Set Theory we can easily enhance our subject ideas.

___________________________________________________________

S.N.	Symbol	Name of Symbol	Definition	Illustration
1	P(A)	Probability Function	Probability of any event A	P(A) = 0.2 or any number between 0 to 1 0 ≤ P (A ≤ 1
2	P(A) = 0	Complete Uncertainty	The event cannot happen	On tossing a coin we shall get prime number.
3	P(A) = 1	Complete certainty	The event will happen definitely	On tossing a die we shall get a number less than 7.
4	P (A ∩ B)	Probability of intersection of events	Probability of Event A and B	P (A ∩ B) = 0.5
5	P (A ⋃ B)	Probability of union of events	Probability of Event A or B	P (A⋃B) = 0.5
6	P (A / B)	Conditional Probability Function	Probability of Event A when B already occurred.	P (A / B) = 0.2 or any number between 0 to 1
7	P (B / A)	Conditional Probability Function	Probability of Event B when A already occurred.	P (B / A) = 0.6 or any number between 0 to 1
8	μ	Mean or population mean	Mean of population values	Mue = 10
9	f(t) or f(x)	pdf	Probability Density function	P (a ≤ t ≤ b) = ∫ f (t) dt, where t is any variable can be replaced by x or y etc.
10	F (t)	cdf	Cumulative distribution function	F(t) = P (T≤ t)
11	E (X)	Expectation Value	Expected value of any random variable x	E (X) = 10
12	E (X / Y)	Conditional Expectation Value	Conditional Expected value of any random variable X given Y	E (X / Y) = 3
13	E (Y/ X)	Conditional Expectation Value	Conditional Expected value of any random variable Y given X	E (Y / X) = 2
14	Sigma 2 (σ 2)	Var(X)	Variance of random variable x	Var(x) = 16
15	∑	Sigma (Capital)	Summation	Sum of all values in the range.
16	∑∑	Sigma (Capital) Sigma (Capital)	Double Summation	Sum of all values in the range.
17	Range	Range	Difference between maximum and minimum value	For series 2, 4, 6, 10, 10, 10, 20,40 Range= 40-2 = 38
18	MR	Mid-range	½(Maximum + Minimum )	For series 2, 4, 6, 10, 10, 10, 20,40 MR= ½(2 + 40) =21
19	Mo	Mode	Value that frequently occurs in data / population / series. Or Maximum number of repetitions	For series 2, 4, 6, 10, 10, 10, 20,40 Mode = 10
20	X bar	Sample Mean / average / Arithmetic Mean	Sum of all observations / No. of observations	For series 2, 4, 6, 10, 10, 10, 20,40 Mean = 1/8 (2+4+6+10+10 +10+20+40)
21	Std(X) or σ(x)	Standard deviation	Standard deviation of random variable x = square root of variance	For any observation, if Var(x) = 16 then Std(X) = 4
22	Median	Median	Mid value of x	For series 2, 4, 6, 10, 10, 10, 20,40 Median = 10
23	cov (x, y)	Covariance	Covariance of any random variable x and y	cov(x, y) = 4
24	corr (x, y)	Correlation	Correlation of any random variable x and y	Corr (x, y) = 4.5
25	ρ(x, y)	Correlation	Correlation of any random variable x and y	ρ (x, y) = 4.5
26	Q	Quartile	% population are below this average on the basis of Q1, Q2, or Q3.
27	Q1	First Quartile / lower	25 % population are below this average or first quartile
28	Q2	Second Quartile / Median	50 % population are below this average
29	Q3	Third Quartile / Upper	25 % population are above this average or 75 % population are below this average

S.N.	Symbol	Name of Symbol	Definition	Illustration
1	{ }	Set	A well-defined collection of objects / elements are known as a set.	A = {1,17,19,24}, B = {3, 7,19,24}, OR C= Set of word MATHEMATICS = {M, A, T, H, E, I, C, S}
2	A = B	equality	both sets have the same members (orders may be different)	A = {1,2,3,4} and B = {1,2,3,4}
3	A ∪ B	union	Those objects which belong to set A or set B.	If A = {1,17,19,24}, and B = {3, 7,19,24}, then A ∪ B = {1, 3, 7, 17, 19, 24}
4	A ∩ B	intersection	Those objects that belong to set A and set B both.	If A = {1,17,19,24}, and B = {3, 7,19,24}, then A ∩ B = {19,24}
5	A ⊆ B	subset	A is a subset of B or set A is included in set B.	{1,2,3,4} ⊆ {1,2,3,4}
6	P ⊂ Q	proper subset or a strict subset	“P is a subset of Q, but Pis not equal to Q”.	{1,2, 4} ⊂ {1,2,3,4}
7	P ⊄ Q	not a subset	"The first (P) set is not a subset of another or second (Q ) set "	{1,2, 4} ⊄ {1,22, 44}
8	P ⊇ Q	superset	P is a superset of Q or set P includes set Q	{1,14,28} ⊇ {1,14}
9	P ⊅ Q	not a superset	set P is not a superset of set Q	{19,14,208} ⊅ {19,23}
10		power set	All subsets of any set like A
11	P (A)	power set	All subsets of any set like A
12		complement	All the objects that do not belong to given set A
13		complement	All the objects that do not belong to given set A
14	A – B	Set A-minus Set B Or relative complement	Objects that belong to set A and but not to set B	If A = {1,2,3,4} and B = {1, 2, 5, 7} then A-B = {3, 4}
15	A / B	Set A minus Set B or relative complement	Objects that belong to set A and but not to set B	If A = {1,2,3,4} and B = {1, 2, 5, 7} then A-B = {3, 4}
16	B – A	Set B minus Set A Or relative complement	Objects that belong to set B and but not to set A	If A = {1,2,3,4} and B = {1, 2, 5, 7} then B- A = {5, 7}
17	B / A	Set B minus Set A or relative complement	Objects that belong to set B and but not to set A	If A = {1,2,3,4} and B = {1, 2, 5, 7} then B- A = {5, 7}
18	a ∈ A	belongs to OR elements of	Element is member of a given set	If A = {1,2,3,4} then 1 ∈ A, 2 ∈ A, 3 ∈ A, 4 ∈ A
19	a ∉ A	Not belongs to OR not element of	Element is NOT a member of given set	If A = {1,2,3,4} then 5 ∉ A
20	A ∆ B	Symmetric difference of sets	Set of all those elements that belong to A or B but not to their intersection. (A ∪ B) – (A ∩ B) OR (A - B) ∪ (B - A)	If A = {1,2,3,4} and B = {1, 2, 5, 7} then A ∆ B = {3,4,5,7}
21	A ⊖ B	Symmetric difference of sets	Set of all those elements that belong to A or B but not to their intersection. (A ∪ B) – (A ∩ B) OR (A - B) ∪ (B - A)	If A = {1,2,3,4} and B = {1, 2, 5, 7} then A ⊖ B = {3,4,5,7}
22	(x, y)	Ordered Pair of x and y	Set of two elements whose order is fixed.
23	A × B	Cartesian Product	it is a set of all possible ordered pairs from A and B
24	B × A	Cartesian Product	Set of all ordered pairs from B and A
25	n (A)	The cardinality of set A	The total number of elements of the set A	A = {1, 2,3,9,14}, n(A) =5
26	\|A\|	The cardinality of set A	The total number of elements of the set A	A = {1, 2,3,9,14}, \|A\|=5
27	(Phi)	Empty Set	The set having No elements.
28	(Zeta)	Universal Set	Superset of all sets

Mathematics

Tuesday, June 30, 2020

Mathematical Symbols - Statistics and Probability

Mathematical Symbols are very important to learn mathematics, on using symbols we can easily understand the concepts of topics.

Generally, Mathematical Symbols can be categorized on their importance in the following ways:

Mathematics symbols - Statistics and Probability

Table of important Mathematical Symbol of Probability and Statistics

On having knowledge of the above Mathematical symbols of probability and statistics, we can easily enhance our subject ideas.

___________________________________________________________

Mathematical Symbols - Set Theory

Mathematical Symbols are very important to learn mathematics, on using symbols we can easily understand the concepts of topics.

Mathematical Symbols can be categorized on their importance in the following ways:

Mathematical symbols - Set Theory

Featured post

Mathematical Symbols - Calculus and Analysis

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Tuesday, June 30, 2020

Mathematical Symbols - Statistics and Probability

Mathematical Symbols are very important to learn mathematics, on using symbols we can easily understand the concepts of topics.

Generally, Mathematical Symbols can be categorized on their importance in the following ways:

Mathematics symbols - Statistics and Probability

Table of important Mathematical Symbol of Probability and Statistics

On having knowledge of the above Mathematical symbols of probability and statistics, we can easily enhance our subject ideas.

___________________________________________________________

Mathematical Symbols - Set Theory

Mathematical Symbols are very important to learn mathematics, on using symbols we can easily understand the concepts of topics.

Mathematical Symbols can be categorized on their importance in the following ways:

Mathematical symbols - Set Theory

Featured post

Mathematical Symbols - Calculus and Analysis

Popular Post

Featured Posts

Total Pageviews