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jaobyccdee
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How to show that the variance of the gaussian distribution using the probability function? I don't know how to solve for ∫r^2 Exp(-2r^2/2c^2) dr .
jaobyccdee said:I tried it. The probability function is 1/(sqrt(2Pi c^2)) * Exp[-r^2/2c] When integrate it from -infinity to infinity, the Exp[r^2] makes everything 0. But we are trying to proof that it's equal to c.
A Gaussian distribution, also known as a normal distribution, is a type of probability distribution that is commonly used in statistics to represent a set of data. It is characterized by a bell-shaped curve and is symmetric around its mean value.
The Gaussian distribution is important in statistics because it is a widely observed natural phenomenon and is used to model many real-world situations. It is also the foundation for many statistical methods and tests, making it a fundamental concept in the field of statistics.
The formula for the Gaussian integral for variance of Gaussian distribution is: Variance = σ2 = ∫-∞∞ (x - µ)2 * e(-x2/2σ2) dx
The Gaussian integral for variance of Gaussian distribution is typically solved using integration techniques, such as substitution or integration by parts. It can also be solved using special functions, such as the error function.
Solving the Gaussian integral for variance of Gaussian distribution allows us to calculate the variance of a set of data that is normally distributed. This is important because the variance is a measure of how spread out the data is, and it can provide valuable insights into the characteristics of the data. It is also used in many statistical tests and analyses to make inferences about a population based on a sample.