Gaussian distribution, also known as normal distribution, is a type of continuous probability distribution that is frequently used in statistics. It is particularly useful in the fields of natural and social sciences, where it is used to represent real-valued random variables. Let's take a closer look at the formula for Gaussian distribution.
Gaussian Distribution Formula: Definition, Explanation, and Solved Examples
Last Updated on Jul 31, 2023
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The Gaussian Distribution Formula
The formula for the probability density function of a Gaussian distribution is as follows:
\[\large f(x,\mu , \sigma )=\frac{1}{\sigma \sqrt{2\pi}}\; e^{\frac{-(x- \mu)^{2}}{2\sigma ^{2}}}\]
Here's what each variable represents:
is the random variable,
represents the mean,
stands for the standard deviation.
Examples
Example 1: Compute the probability density function of a Gaussian distribution given the following parameters: x = 3,
= 4 and
= 2.
Solution:
Given that x = 3,
= 4 and
= 2, the probability density function of a Gaussian distribution can be computed as follows:
f(x,
,
) =
So, f(3, 4, 2) =
= [1/(2 × 2.51)] × 0.8825
= 0.1994 × 0.8825
= 0.1761
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Frequently Asked Questions
What is the formula for Gaussian Distribution?
The formula for Gaussian Distribution is f(x,μ,σ) = 1/σ√2π * e^(-(x-μ)^2/2σ^2)
What does 'x', 'μ', and 'σ' represent in the Gaussian Distribution formula?
In the Gaussian Distribution formula, 'x' is the variable, 'μ' is the mean, and 'σ' is the standard deviation.
How to calculate the probability density function of Gaussian distribution?
The probability density function of Gaussian distribution can be calculated using the formula f(x,μ,σ) = 1/σ√2π * e^(-(x-μ)^2/2σ^2). Plug in the given values of x, μ, and σ in the formula to get the result.
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