Probability and Statistics Symbols

Probability and Statistics Symbols

You can explore Probability and Statistics Symbol’s, names meanings and examples below-

Symbol	Symbol Name	Meaning / definition	Example
P(A ∩ B)	probability of events intersection	probability that of events A and B	P(A∩B) = 0.5
P(A)	probability function	probability of event A	P(A) = 0.5
P(A | B)	conditional probability function	probability of event A given event B occurred	P(A | B) = 0.3
P(A ∪ B)	probability of events union	probability that of events A or B	P(A∪B) = 0.5
F(x)	cumulative distribution function (cdf)	F(x) = P(X ≤ x)
f (x)	probability density function (pdf)	P(a ≤ x ≤ b) = ∫ f (x) dx
E(X)	expectation value	expected value of random variable X	E(X) = 10
μ	population mean	mean of population values	μ = 10
var(X)	variance	variance of random variable X	var(X) = 4
E(X | Y)	conditional expectation	expected value of random variable X given Y	E(X | Y=2) = 5
std(X)	standard deviation	standard deviation of random variable X	std(X) = 2
σ2	variance	variance of population values	σ2 = 4
x˜	median	middle value of random variable x	x˜=5<
σX	standard deviation	standard deviation value of random variable X	σX  = 2
corr(X,Y)	correlation	correlation of random variables X and Y	corr(X,Y) = 0.6
cov(X,Y)	covariance	covariance of random variables X and Y	cov(X,Y) = 4

Geometry Symbol

Geometry Symbol 

Let’s explore the typical Geometry symbols and meanings used in both basic Geometry and more advanced levels through this geometry symbol chart.

Symbol	Symbol Name	Meaning/definition of the Symbols	Example
∠	measured angle		ABC = 30º
∠	angle	formed by two rays	∠ABC = 30º
∟	right angle	= 90º	α = 90º
	spherical angle		AOB = 30º
´	arcminute	1º = 60´	α = 60º59′
º	degree	1 turn = 360º	α = 60º
´´	arcsecond	1´ = 60´´	α = 60º59’59”
AB−→−<	ray	line that start from point A
AB	line segment	the line from point A to point B
|	perpendicular	perpendicular lines (90º angle)	AC | BC
≅	congruent to	equivalence of geometric shapes and size	∆ABC ≅∆XYZ
||	parallel	parallel lines	AB || CD
Δ	triangle	triangle shape	ΔABC ≅ΔBCD
~	similarity	same shapes, not the same size	∆ABC ~∆XYZ
π	pi constant	π = 3.141592654… is the ratio between the circumference and diameter of a circle	c = π·d = 2·π·r
|x–y|	distance	distance between points x and y	| x–y | = 5
grad	grads	grads angle unit	360º = 400 grad
rad	radians	radians angle unit	360º = 2π rad

Algebra Symbols

Algebra Symbols

Algebra Symbols With Names

Let’s explore the names of common algebra symbols used in both basic algebra and more advanced levels.

Symbol	Symbol Name	Meaning/definition	Example
≡	equivalence	identical to
x	x variable	unknown value to find	when 2x = 4, then x = 2
:=	equal by definition	equal by definition
≜	equal by definition	equal by definition
≈	approximately equal	approximation	sin(0.01) ≈ 0.01
~	approximately equal	weak approximation	11 ~ 10
∞	lemniscate	infinity symbol
∝	proportional to	proportional to	y ∝ x when y = kx, k constant
≫	much greater than	much greater than	1000000 ≫ 1
≪	much less than	much less than	1 ≪ 1000000
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
( )	parentheses	calculate expression inside first	2 * (3+5) = 16
⌊x⌋	floor brackets	rounds number to lower integer	⌊4.3⌋= 4
{ }	braces	set
			5

Set theory

Set theory

Set theory was developed to explain about collections of objects, in Maths. Basically, the definition states it is a collection of elements. These elements could be numbers, alphabets, variables, etc. The notation and symbols for sets are based on the operations performed on them. You must have also heard of subset and superset, which are the counterpart of each other.

Symbols Used For Representation of Sets

Let us see the different types of symbols we used while we learn about sets. Consider a Universal set (U) = {1, 2, 7, 9, 13, 15, 21, 23, 28, 30}

Symbol	Symbol Name	Meaning / definition	Example
{ }	set	a collection of elements	A = {1, 7, 9, 13, 15, 23}, B = {7, 13, 15, 21}
A ∪ B	union	objects that belong to set A or set B	A ∪ B = {1, 7, 9, 13, 15, 21, 23}
A ∩ B	intersection	objects that belong to both the sets, A and B	A ∩ B = {7, 13, 15 }
A ⊆ B	subset	subset has few or all elements equal to the set	{7, 15} ⊆ {7, 13, 15, 21}
A ⊄ B	not subset	left set not a subset of right set	{1, 23} ⊄ B
A ⊂ B	proper subset / strict subset	subset has fewer elements than the set	{7, 13, 15} ⊂ {1, 7, 9, 13, 15, 23}
A ⊃ B	proper superset / strict superset	set A has more elements than set B	{1, 7, 9, 13, 15, 23} ⊃ {7. 13. 15. }
A ⊇ B	superset	set A has more elements or equal to the set B	{1, 7, 9, 13, 15, 23} ⊃ {7. 13. 15. 21}
Ø	empty set	Ø = { }	C = {Ø}
P (C)	power set	all subsets of C	C = {4,7}, P(C) = {{}, {4}, {7}, {4,7}} Given by 2s, s is number of elements in set C
A ⊅ B	not superset	set A is not a superset of set B	{1, 7, 9, 13, 15, 23} ⊅{7, 13, 15, 21}
A = B	equality	both sets have the same members	{7, 13,15} = {7, 13, 15}
A \ B or A-B	relative complement	objects that belong to A and not to B	{1, 9, 23}

Types of sets

Types of sets

Empty Set 

The set which is empty! This means that there are no elements in the set. This set is represented by ϕ or {}. An empty set is hence defined as:

Definition: If a set doesn’t have any elements, it is known as an empty set or null set or void set. For e.g. consider the set

P = {x : x is a leap year between 1904 and 1908}

Between 1904 and 1908, there is no leap year. So, P = ϕ. Similarly, the set

Q = {y : y is a whole number which is not a natural number,y ≠ 0}

0 is the only whole number that is not a natural number. If y ≠ 0, then there is no other value possible for y. Hence, Q = ϕ.

Singleton Set

If a set contains only one element, then it is called a singleton set. For e.g.

A = {x : x is an even prime number}

B={ y : y is a whole number which is not a natural number}

Finite Set

In this set, the number of elements is finite. All the empty sets also fall into the category of finite sets.

Definition: If a set contains no element or a definite number of elements, it is called finite set.

If the set is non-empty, it is called a non-empty finite set. Some examples of finite sets are:
A = {x : x is a month in an year}; A will have 12 elements

B={y: y is the zero of a polynomial (x4 − 6x2 + x + 2)}; B will have 4 zeroes

Infinite Set

Just contrary to the finite set, it will have infinite elements. If a given set is not finite, then it will be an infinite set.

For e.g.
A = {x : x is a natural number}; There are infinite natural numbers. Hence, A is an infinite set.

B = {y: y is ordinate of a point on a given line}; There are infinite points on a line. So, B is an infinite set.

Power Set

An understanding of what subsets are is required before going ahead with Power-set.

Definition: The power set of a set A is the set which consists of all the subsets of the set A. It is denoted by P(A).

For a set A which consists of n elements, the total number of subsets that can be formed is 2n. From this, we can say that P(A) will have 2n elements. For e.g.

Universal Set

This is the set which is the base for every other set formed. Depending upon the context, the universal set is decided. It may be a finite or infinite set. All the other sets are the subsets of the Universal set. It is represented by U.

For e.g. The set of real numbers is a universal set of integers. Similarly, the set of a complex number is the universal set for real numbers.