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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
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
18
MR
Mid-range
½(Maximum + Minimum )
For series 2, 4, 6, 10, 10, 10, 20,40
19
Mo
Mode
Value that frequently occurs in
data / population / series. Or
For series 2, 4, 6, 10, 10, 10, 20,40
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
21
Std(X) or
Standard deviation
Standard deviation of random
variable x = square root of variance
For any observation, if Var(x) = 16
then
22
Median
Median
Mid value of x
For series 2, 4, 6, 10, 10, 10, 20,40
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
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.
On having knowledge of the above Mathematical symbols of probability and statistics, we can easily enhance our subject ideas.
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