03. Introduction to the normal distribution

Understanding Normal Distribution

The normal distribution, commonly known as the Gaussian distribution, is a vital concept in statistics and financial modeling.

• Characteristics:

  • Bell-Shaped Curve: Symmetrical around the mean.
  • Mean (Mu): The center of the curve.
  • Standard Deviation (Sigma): Determines the width of the bell shape.
  • Variance (Sigma squared): Measures the spread of data.

• Notations:

  • N(μ, σ²): Represents a normal distribution with a mean (μ) and variance (σ²).
  • Expected Value: Equal to the mean of the distribution

• Calculations:

  • Mean Calculation: Sum all data points and divide by the number of points.
  • Variance: Calculate the squared deviation from the mean, average these values.
  • Standard Deviation: The square root of variance, showing data spread.

These concepts help describe and predict data behavior across various fields.