Chapter 3: Probability and Statistical Distributions

This chapter discusses basic foundational principles, including probability and basic descriptive statistics. It also introduces several important probability distribution functions.

Sum of Probabilities

Joint and Conditional Probabilities

A 2x2 Contingency Table

Transformation of Distribution

Flux Errors

Kurtosis and Skew

Example of a uniform distribution

Example of a Gaussian distribution

Example of a Binomial distribution

Example of a Poisson distribution

Example of a Cauchy distribution

Median and Mean for Cauchy distribution

Example of a Laplace distribution

Example of a chi-squared distribution

Example of Student’s t distribution

Example of Fisher’s F distribution

Example of a Beta distribution

Example of a Gamma distribution

Example of a Weibull distribution

Example of central limit theorem

Convergence of mean for uniformly distributed values

Bivariate Gaussian

Bivariate Gaussian: Robust Parameter Estimation

Correlation estimates

Random Values from an Empirical Distribution