The normal distribution is characterized by its bell-shaped curve, symmetric around the mean value (μ), with its spread determined by the standard deviation (σ).
The probability density function (pdf) of a normal distribution is given by the following equation:
f(x) = (1 / sqrt(2πσ^2)) * exp(-(x – μ)^2 / (2σ^2))
In this equation:
- x is the random variable.
- μ (mu) represents the mean value, which indicates the center of the distribution.
- σ (sigma) represents the standard deviation, which determines the spread or dispersion of the distribution.
- π is the mathematical constant pi (approximately 3.14159).
- exp() denotes the exponential function, which is equivalent to raising the base of the natural logarithm (e) to a power. For example, exp(x) is the same as e^x.
The normal distribution is applicable to many data sets in nature and social phenomena, and its properties have been extensively studied. Additionally, the Central Limit Theorem states that the sum of a large number of independent random variables approaches a normal distribution.
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