Gaussian Distribution Formula

Gaussian distribution is very common in a continuous probability distribution. The Gaussian distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables. Check out the Gaussian distribution formula below.

Formula of Gaussian Distribution

The probability density function formula for Gaussian distribution is given by,

f(x,μ,σ)=1σ2πe−(x−μ)22σ2

Where,

x
is the variable

μ
is the mean

σ
is the standard deviation

Solved Examples

Question 1: Calculate the probability density function of Gaussian distribution using the following data. x = 2,

μ
= 5 and
σ
= 3

Solution:

From the question it is given that, x = 2,

μ
= 5 and
σ
= 3

Probability density function formula of Gaussian distribution is,

f(x,

μ
,
σ
) =
1σ2π
e−(x−μ)22σ2

f(2, 5, 3 ) =

1σ2π
e−(2−5)218

=[1/(3 ×2.51) ] × 0.6065

= 0.1328 ×0.6065

= 0.0805

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