Lectures related to Probabilities and Statistics: Key Theorems and Applications

Probability and Statistics: Fundamentals

Covers the fundamental concepts of probability and statistics, including interesting results, standard model, image processing, probability spaces, and statistical testing.

Estimating R: Moments of a Distribution

Explains the importance of moments in measuring distribution properties, such as expectation and variance.

Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.

Linear Combinations: Moment-Generating Functions

Explores moment-generating functions, linear combinations, and normality of random variables.

Conditional Expectation: Grouping Lemma

Explores conditional expectation, the grouping lemma, and the law of large numbers.

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

Probability and Statistics

Covers moments, variance, and expected values in probability and statistics, including the distribution of tokens in a product.

Convergence of Random Variables

Explores different modes of convergence for random variables.