The Gaussian Distribution is pretty common in the case of continuous probability distribution. The distribution is frequently used in statistics and it is generally required in natural or social sciences to showcase the real-valued random variables. The probability density formula for Gaussian Distribution in mathematics is given as below –

\[\large f(x,\mu , \sigma )=\frac{1}{\sigma \sqrt{2\pi}}\; e^{\frac{-(x- mu)^{2}}{2\sigma ^{2}}}\]

Where,

x is the variable

μ is the mean

sigma is the standard deviation

You must be wondering what is the usage of Gaussian functions in statistics. They are used to describe the normal distributions and signal processing for images. They are also required in the heat transfer and diffusion of equations to define the wire transformation.

If the number of events is very large then Gaussian distribution is particularly suitable for various physical events too. This is a continuous function that give you an idea of exact distribution of binomial events.

This concept is valid for normalized equations too when sun over all values of x define the probability of one. It is somehow related to the standard deviation of mean too. The other name for Gaussian distribution is the normal distribution that is usually defined as the bell-shaped curve.

The formula is designed to evaluate different mathematical concepts like mean value, standard deviation, and the value of distribution function too where the value of x is supplied. The concept is valid for a large number of distributions too for evaluating the precise results.

Further, the concept is necessary in discrete applications too particularly to process the digital signatures. The simple answer to each of your problem is Gaussian distribution yielding the best outcomes as needed.