Gaussian PDF

The Gaussian Probability Density Function (PDF), also known as the Normal Distribution, is a commonly used statistical distribution that describes the probability of a continuous random variable. The Gaussian distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ).

The PDF of a Gaussian distribution is given by the following equation:

f(x) = (1/σ√(2π)) exp(-(x-μ)²/(2σ²))

where x is the random variable, σ is the standard deviation, μ is the mean, and exp is the exponential function.

The Gaussian PDF is symmetric around its mean, with the highest probability density occurring at the mean. As the standard deviation increases, the curve of the distribution becomes flatter and wider. The total area under the curve is equal to one, which means that the probability of any value occurring is between zero and one.

The Gaussian distribution is widely used in various fields, including physics, engineering, finance, and social sciences, due to its simplicity and versatility. It is often used to model natural phenomena, such as the distribution of measurement errors, noise, or random fluctuations.