Binomial distribution with example

What is Binomial Distribution

    Binomial Distribution is also called as Bernoulli's Distribution. Let X be Binomially Distributed with the parameter 'n' and 'p'.

P(X) = nC_x  p^xq^n-x

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In chance idea and statistics, the binomial distribution with parameters n and p is the discrete chance distribution of the variety of successes in a sequence of n independent experiments.

Every asking a sure–no question, and each with its very own boolean-valued final results: a random variable containing single bit of records: achievement/sure/actual/one (with opportunity p) or failure/no/false/zero (with probability q = 1 − p).

A unmarried achievement/failure experiment is also referred to as a Bernoulli trial or Bernoulli experiment and a series of results is known as a Bernoulli process, for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution.

The binomial distribution is the premise for the popular binomial check of statistical significance.

The binomial distribution is regularly used to version the range of successes in a pattern of length n drawn with substitute from a populace of length n. 

If the sampling is performed without substitute, the draws aren't independent and so the ensuing distribution is a hyper-geometric distribution, no longer a binomial one. But, for n a great deal larger than n, the binomial distribution remains a good approximation, and is widely used.

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Note:

1. Mean = E(X) = np
2. Variance =  σ²   = npq

Logarithms and Exponent:e power infinity,e power minus infinity,etc

What is Logarithms

Logarithms is the power which a number must be raised order to get some other number.

log_bn=r

Example 1:

log₁₀ 1000 = 3

L.H.S = log₁₀ 1000

log₁₀10³

3log₁₀10=3

log₁₀ 1000 = 3

Example 2:

log₅ 25 = 2

L.H.S = log₅ 25

log₅₅²

2log₅5=2

log₅ 25 = 2

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What is Antiogarithms

Antilogarithms is the inverse of the logarithms it is used to raise the value of the given number from the base.

Example:

Antilog_bx=1/log_bx


Antilog_bx(log_bx)=x

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What is Exponent

Exponent of the number says how many times to use that number in a multiplication it is return as a small number to right and above the base number.

Example 1:

₈²_{=8 x 8=64}

• Here 2 is the exponent
• It is user wise called index or power

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What is e power infinity ?

 Where e is the constant number and infinity is the maximum number. When e is raised(power) into infinity is equal to infinity.

In the basis of anything power infinity is equal infinity.(_n^infinity_=infinity)

n is the constant number

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What is e power minus infinity ?

 Where e is the constant number and infinity is the maximum number. When e is raised(power) into minus infinity is equal to 0.

In the basis of anything power infinity is equal infinity.(_n^-infinity₌₀₎

n is the constant number

Example:

₅^-3 = 0.005

₅^-infinity = 0.000.......05 approximately is 0

How to Find Area and Volume Using Measurements:Rectangle, Cylinder, Triangle, Cone, Circle, Sphere

Formula to find Area and Volume

Define Area:

Area is the size of a two-dimensional surface.he mathematical term 'area' can be defined as the amount of two-dimensional space taken up by an object.  This lesson will define area, give some of the most common formulas, and give examples of those formulas.

Define Volume:

It is the size of three dimensional surface. Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, etc. It's units are always "cubic", that is, the number of little element cubes that fit inside the figure. 

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Rectangle :

In two dimension

area : l x b 

l = length

b= breath

In Three dimension:

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Triangle:

In two dimension

area=bh/2

l=length

b=breath

h=height

In Three dimension:

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Circle:

In two dimension

r=radius

π=22/7

r=d/2

d=diameter

In Three dimension:

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Semi sphere:

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Conversion of Cone:

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Matrix Properties:Symmetric Matrix, Skew Symmetric Matrix,Hermitian Matrix,Row,Column,Diagonal

Types of Matrix

Row Matrics	( 1 2 3)
Column Matrics	1    2    3
Square Matrics (m=n)	1   2  3   4
Diagonal Matrics	1   0    0   2  1  0  0  0  2  0  0  0  3
Identity Matrics or Unit Matrics	4  0  0  0  4  0  0  0  4
Transpose of the Matrics	A=   1  2         3  4 AT  = 1  3           2  4

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Symmetric Matrics

A Square Matrics "A" is said to be a symmetric Matrics is the Transpose of the Matrics is equal to the "A-Matrix".

A^t = A

Example:

        1   4    6

A = 4   2   -5

       6   -5   3

         1   4    6

A^t =  4   2    -5

        6   -5    3

A^t  =  A

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Skew Symmetric Matrix

A Square matrix "A" is said to be a Skew symmetric of the transpose as the matrix is equal to -A.

Example:

A^t  =  -A

         0   -4   6
A  = 4   0   -5
      -6    5   0

          0   4   6
A^t =  -4   0   -5
         -6    5   0



A^t  =  -A

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Hermitian Matrix

A Square Matrix "A" is said to be Hermitian, if the conjugate transpose of the matrix is equal to the matrix itself 

Example:

_          
A^t  =  A


           1   4+i   6i
A=    4i    2     -5

                         -6i    -5    3                 

_         1    4i    6i
A=     4+i    2     -5
                -6i     -5     3        


_       1   4+i   6i
A^t =    4i    2     -5
                        -6i    -5    3                 

 _          
A^t  =  A

     

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Skew Hermitian Matrix

A square matrix "A" is said to be skew Hermitian of the conjugate of transpose of the matrix is equal to   

                                                _          

A^t  =  -A

Example:

                0   4+i   -1+6i
A=    4+i    2     -5

                         1+6i    -5    0                

        _         0    -4-i    -1-6i
A=      4-i     0     -5

                     1+6i    -5     0        

     _          0   -4-i   1-6i
A^t =     -4-i    0     5

                            -1-6i    -5    0                

                                               _          

A^t  =  -A

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Orthogonal Matrix:

A Square matrix "A" is said to be orthogonal matrix

AA^t =I 

  

Fast Multiplication Tricks:Find it in 10 sec with 5,25,125

Don’t fear about math or a multiplication of numbers doing manually it have to calculate in our mind.  One of that method is explained Here.  Using this trick you can multiply any number with number end with 5,25,125, etc. For your thoughts it is certainly try this typically it's miles tough to multiply  6734 x 25 = ?
using this trick you may do that in five seconds
 

For More Understanding watch this video to clarify

 Practice Makes you Perfect

Exercise makes you ideal

Comment Your Question

Pythagoras theorem (Baudhayan theorem)

How to find the cube root of the Numbers within 3 seconds

Easiest and Shortest way to find the Cube Root

Define Cube Root ?

      Cube Root is the Number Which is the Multiple of same number three times to get it.

Example 1:

4 X 4 X 4 = 64

Here, 64 is the Cube value 

4 is the Cube Root of 64.


Example 2:

7 X 7 X 7 = 343

Here, 343 is the Cube Value

7 is the Cube Root of 343.

General way to find it is:

         Using the L.C.M to find the Cube Root 

• First find LCM  a value of the Given Number
• Then taking it out with the three repeated Number
• Then Muliply the Resultent Number To get the Cube Root Number.

Example 1:

what us the Cube Root of  64

          ³⎷64

2ட64

2ட32

2ட16

2ட8

2ட4

2ட2

          ³⎷64 = ³⎷2 X 2 X 2 X 2 X 2 X 2  = 2 X 2 X 2

                

              ³⎷64 = 8

Hence Cube Root of 64 is 8

Example 2:

 what is the Cube Root of  343

         ³⎷343  

7ட343

7ட49

7ட7

 ³⎷343  =  ³⎷ 7 X 7 X 7  = 7


Hence Cube Root of 343 is 7

In the case of larger numbers like 9,70,299  6,36,056

There was a Trick to find a Cube roots Easily with in the 3 seconds:

First we want to memorize This Table

Cube Root	Cubed Values
1 3	1
2 3	8
3 3	27
4 3	64
5 3	125
6 3	216
7 3	343
8 3	512
9 3	729
10 3	1000

For Example Take 6,36,056

1. See the last digit in the  Cubed Values, Which was 6

Which is the Last Digit of the Cube root value

6 3

216

We have to memories this in another way
  Last Digit is same for  1,4,5,6,9,0    Flips for 2 & 8,  3 & 7
2. Then Omit last Three digits and find the nearest Cube root for the remaining
The remaining Numbers are 636 - The Nearest Cube Root is 8
It is the First Digit of the Cube Root Value
Hence it was the result
Cube Root of 636056 is 86
 ³⎷6,36,056 = 86     Now you learned it 
If  you have any doubt ask it in comment