Probability Theory: Midterm Solutions

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Conditional Density and Expectation

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

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Probability and Statistics

Covers fundamental concepts in probability and statistics, including distributions, properties, and expectations of random variables.

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Transformations of Joint Densities

Covers the transformations of joint continuous densities and their implications on probability distributions.

Normal Distribution: Properties and Calculations

Covers properties and calculations related to the normal distribution, including probabilities and quantiles.

Conditional Probability: Prediction Decomposition

Explores conditional probability, Bayes' theorem, and prediction decomposition for informed decision-making.