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,
\[\large f(x,\mu , \sigma )=\frac{1}{\sigma \sqrt{2\pi}}\; e^{\frac{-(x- \mu)^{2}}{2\sigma ^{2}}}\]
Where,
Solved Examples
Question 1: Calculate the probability density function of Gaussian distribution using the following data. x = 2,
Solution:
From the question it is given that, x = 2,
Probability density function formula of Gaussian distribution is,
f(x,
f(2, 5, 3 ) =
=[1/(3 ×2.51) ] × 0.6065
= 0.1328 ×0.6065
= 0.0805
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