Understanding Normal Distribution

Statistics in R

Introduction

Normal distribution, also known as the Gaussian distribution or bell curve, is a fundamental concept in statistics and probability theory. It describes a symmetrical, bell-shaped probability distribution characterized by its mean (average) and standard deviation. The normal distribution is essential in various fields, including finance, biology, psychology, and quality control.

In a normal distribution:

The mean (μ) represents the central location of the distribution.

The standard deviation (σ) controls the spread or dispersion of the distribution.

The curve is symmetric, with tails extending infinitely in both directions.

Probability Density Function (PDF) of Normal Distribution

The probability density function of a normal distribution is given by the formula:

where,

• f(x∣μ,σ) is the probability density function.
• μ is the mean of the distribution.
• σ is the standard deviation of the distribution.
• e is the base of the natural logarithm.

In R, you can generate random numbers following a normal distribution using the…