Introduction to Sum of Uniform Distributions:
Uniform distributions is the part of the probability distributions, It is one of the simplest way of distributions. The Sum of uniform distributions is also known as uniform random distributions. Uniform random distributions is analysis numerical data value.That datas are arranged in systamatically.In this article we see the types of uniform distributions, and some example problems of the sum of uniform distributions.
Types of Uniform Distributions:
Sum of Uniform Distributions has three types ,there are
Continues Uniform Distributions
Discrete Uniform Distributions
1.Continues Uniform Diostributions:
The continues uniform distributions is the density function of the random variable. Continues interval between a and b. The density function of continues uniform distribution is ,
` [ f(x) = {( 1/ (b-a) when a<= x <= b) , ( 0 when xb):} ]`
Now see the graph of continues uniform distributions with a=1, b=3
2.Discrete Uniform Distributions :
Discrete distributions are also known as statistical distributions, It is the simplest way of Probability distribution functions.
Discrete distribution of Probability distributions functions of p(Xm) is defined over m= 1,2,….,N ,
The discrete distribution function as
D(Xn)= ∑ p(Xm)
Uniform Random Distribution General Formula:
The general formula of probability density function of the uniform random distribution function is defined as follows:
f(x) = 1 /b-a for a` <=` x `<= ` b
Where a is the position parameter and (b-a) is the scale parameter. In case where a = 0 and b = 1 is called the standard uniform random distribution.
The equation of the standard uniform random distribution is
f(x) = 1 for 0 ` <=` x `<= ` 1.
These all are important in the Uniform random distributions. Is this topic how do you determine if a polynomial is the difference of two squares? hard for you. Watch out for my coming posts.
Examples Problems for the Sum of Uniform Distributions
Example 1:
f(x) = 6x^3+8 for 0 x 1. Find the expected value continuous of given f(x).
Solution:
E (X) = X’ = x f(x) dx
= x (6`x^3` +8) dx
= (6`x^3` +8x) dx
= [6`x^4` /4 + 8`x^2` /2]
=6/4+8/2 – 0 -0
E(X) = 22/4 = 5.5
Example 2:
f(x) = x^3+4x^2 for 0 x 1. Find the expected value continuous of given f(x).
Solution:
E (X) = X’ = x f(x) dx
= x (`x^3` +4`x^2` ) dx
= (`x^4` +4`x^2` ) dx
= [`x^5` /5 + 4 `x^3` /3]
= 1/5 +4/3 -0 -0
E(X) = 23/15 = 1.5333
Exercise Problems for the Sum of Uniform distributions
Problem -1: f(x) = 8x for 0 x 1. Find the expected value continuous of given f(x).
Answer: 2.6667
Problem -2: f(x) = `x^2` (2`x^4` ) for 0 x 1. Find the expected value continuous of given f(x).
Answer: 0.25
Problem -3: f(x) = (`4x)^3` for 0 x 1. Find the expected value continuous of given f(x).
Answer: 12.8
Uniform distributions is the part of the probability distributions, It is one of the simplest way of distributions. The Sum of uniform distributions is also known as uniform random distributions. Uniform random distributions is analysis numerical data value.That datas are arranged in systamatically.In this article we see the types of uniform distributions, and some example problems of the sum of uniform distributions.
Types of Uniform Distributions:
Sum of Uniform Distributions has three types ,there are
Continues Uniform Distributions
Discrete Uniform Distributions
1.Continues Uniform Diostributions:
The continues uniform distributions is the density function of the random variable. Continues interval between a and b. The density function of continues uniform distribution is ,
` [ f(x) = {( 1/ (b-a) when a<= x <= b) , ( 0 when xb):} ]`
Now see the graph of continues uniform distributions with a=1, b=3
2.Discrete Uniform Distributions :
Discrete distributions are also known as statistical distributions, It is the simplest way of Probability distribution functions.
Discrete distribution of Probability distributions functions of p(Xm) is defined over m= 1,2,….,N ,
The discrete distribution function as
D(Xn)= ∑ p(Xm)
Uniform Random Distribution General Formula:
The general formula of probability density function of the uniform random distribution function is defined as follows:
f(x) = 1 /b-a for a` <=` x `<= ` b
Where a is the position parameter and (b-a) is the scale parameter. In case where a = 0 and b = 1 is called the standard uniform random distribution.
The equation of the standard uniform random distribution is
f(x) = 1 for 0 ` <=` x `<= ` 1.
These all are important in the Uniform random distributions. Is this topic how do you determine if a polynomial is the difference of two squares? hard for you. Watch out for my coming posts.
Examples Problems for the Sum of Uniform Distributions
Example 1:
f(x) = 6x^3+8 for 0 x 1. Find the expected value continuous of given f(x).
Solution:
E (X) = X’ = x f(x) dx
= x (6`x^3` +8) dx
= (6`x^3` +8x) dx
= [6`x^4` /4 + 8`x^2` /2]
=6/4+8/2 – 0 -0
E(X) = 22/4 = 5.5
Example 2:
f(x) = x^3+4x^2 for 0 x 1. Find the expected value continuous of given f(x).
Solution:
E (X) = X’ = x f(x) dx
= x (`x^3` +4`x^2` ) dx
= (`x^4` +4`x^2` ) dx
= [`x^5` /5 + 4 `x^3` /3]
= 1/5 +4/3 -0 -0
E(X) = 23/15 = 1.5333
Exercise Problems for the Sum of Uniform distributions
Problem -1: f(x) = 8x for 0 x 1. Find the expected value continuous of given f(x).
Answer: 2.6667
Problem -2: f(x) = `x^2` (2`x^4` ) for 0 x 1. Find the expected value continuous of given f(x).
Answer: 0.25
Problem -3: f(x) = (`4x)^3` for 0 x 1. Find the expected value continuous of given f(x).
Answer: 12.8
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