Continuous Random VariablesExplores continuous random variables, density functions, joint variables, independence, and conditional densities.
Discrete Random VariablesCovers properties and transformations of discrete random variables, focusing on PMF and expectation.
Statistical EstimationCovers statistical estimation methods and explores practical examples of parameter estimation for different distributions.
Probability and StatisticsCovers p-quantile, normal approximation, joint distributions, and exponential families in probability and statistics.
Stellar Systems DynamicsExplores stellar systems dynamics, covering models, equations, and velocity distributions in spherical and cylindrical coordinates.
Data Loading and FilteringCovers loading compressed files, filtering dataframes, and analyzing data distribution for effective analysis.
Optimality in Statistical InferenceDelves into the duality between confidence intervals and hypothesis tests, emphasizing the importance of precision and accuracy in estimation.
Collisionless Boltzmann EquationExplores the Collisionless Boltzmann equation, distribution functions, Jeans theorems, resonances, chaotic orbits, and equilibria in stellar systems.
Calculations of ExpectationCovers the calculation of expectation and variance for different types of random variables, including discrete and continuous ones.