Unified spheric propability

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In summary, Unified Spheric Probability is a mathematical theory that considers all possible outcomes of an experiment as equally likely, regardless of prior knowledge or assumptions. It differs from traditional probability by providing a more objective and comprehensive approach to understanding uncertainty. The purpose of Unified Spheric Probability is to provide a more realistic and unbiased evaluation of results and predictions in scientific experiments. It can be applied to any field that involves uncertainty and probability and there are many resources available to learn more about it.
  • #1
yetar
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Lets say we have as much as 1D uniform random variables we want.
How from these 1D uniform random variable, we can create a uniform random variable upon the shell of a sphere?
 
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  • #2
I have solved the problem.
To get a unified spherical surface random variable you need to do the following:
Given Y and teta are unified random variables each.
The random variable F(Y, teta) = (Sqrt(r^2-Y^2)*sin(teta), Y, Sqrt(r^2-Y^2)*cos(teta))
Gives a unified sphere surface random variable.
 
  • #3


The concept of unified spheric probability is a fascinating one, and it offers a way to create a uniform random variable on the shell of a sphere using 1D uniform random variables. This can be achieved through a process called spherical coordinate transformation.

To understand this process, let's first consider the 1D uniform random variable. This type of random variable takes on values between 0 and 1 with equal probability for each value. Now, imagine we have a sphere with a radius of 1. We can define the shell of this sphere as all points on its surface, which are at a distance of 1 from its center.

To create a uniform random variable on this shell, we need to map the 1D uniform random variable onto the surface of the sphere. This is where the spherical coordinate transformation comes into play. This transformation takes the 1D variable and converts it into a set of three coordinates: radius, inclination, and azimuth.

The radius coordinate is simply the distance from the origin to the point on the surface of the sphere. In our case, this is always a constant value of 1. The inclination and azimuth coordinates determine the position of the point on the surface of the sphere.

By using this transformation, we can map the 1D uniform random variable onto the surface of the sphere, creating a uniform distribution of points on the shell. This means that every point on the shell has an equal chance of being selected, just like a 1D uniform random variable.

In conclusion, the concept of unified spheric probability allows us to create a uniform random variable on the shell of a sphere using 1D uniform random variables. This is achieved through the use of spherical coordinate transformation, which maps the 1D variable onto the surface of the sphere. This method can be extended to higher dimensions as well, making it a powerful tool in probability and statistics.
 

1. What is Unified Spheric Probability?

Unified Spheric Probability is a mathematical theory that aims to unify the principles of probability and statistics by considering all possible outcomes of an experiment as equally likely, regardless of prior knowledge or assumptions.

2. How is Unified Spheric Probability different from traditional probability?

Traditional probability assigns probabilities based on prior knowledge and assumptions, while Unified Spheric Probability considers all possibilities as equally likely. This allows for a more objective and comprehensive approach to understanding uncertainty.

3. What is the purpose of Unified Spheric Probability?

The purpose of Unified Spheric Probability is to provide a more realistic and unbiased approach to understanding uncertainty in scientific experiments and observations. It allows for a more precise and comprehensive evaluation of results and predictions.

4. Can Unified Spheric Probability be applied to any scientific field?

Yes, Unified Spheric Probability can be applied to any scientific field that involves uncertainty and probability. It has been used in fields such as physics, biology, and economics to provide a more comprehensive understanding of data and results.

5. How can I learn more about Unified Spheric Probability?

There are many resources available to learn more about Unified Spheric Probability, including books, online articles, and courses. You can also consult with experts in the field or attend conferences and workshops to deepen your understanding of this theory.

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