Conditional expectation

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Statistical Theory: Fundamentals

Covers the basics of statistical theory, including probability models, random variables, and sampling distributions.

Probability Theory: Midterm Solutions

Covers the solutions to the midterm exam of a Probability Theory course, including calculations of probabilities and expectations.

Expectation: Basic Properties

Discusses integrability, square-integrability, boundedness, centering, and linearity of random variables.

Transformations of Random Variables

Covers the pdf of the sum of continuous random variables, convolution, and transformations like Y=aX.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Conditional Density and Expectation

Explores conditional density, expectations, and independence of random variables with practical examples.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Calculations of Expectation

Covers the calculation of expectation and variance for different types of random variables, including discrete and continuous ones.

Entropy and Data Compression: Huffman Coding Techniques

Discusses entropy, data compression, and Huffman coding techniques, emphasizing their applications in optimizing codeword lengths and understanding conditional entropy.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.