Normal distribution

The normal distribution, also known as Gaussian distribution, is a fundamental concept in probability theory and statistics. Its probability density function (PDF) is crucial for understanding the distribution of continuous data.

The formula for the normal distribution PDF is given by:

f(x) = (1 / (σ√(2π))) * exp(-((x - μ)² / (2σ²)))

In this formula, μ represents the mean of the distribution, σ represents the standard deviation, and exp denotes the exponential function. The constant (1 / (σ√(2π))) is the normalization factor that ensures the total area under the curve equals 1.

Understanding the normal distribution PDF is essential for various applications in statistics, such as hypothesis testing, confidence intervals, and data analysis. It helps in determining probabilities and making inferences about population parameters based on sample data.