Presbycusis 发表于 2025-3-23 13:05:30

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有罪 发表于 2025-3-23 15:32:06

Surfaces with Riemannian Metric,The best we can do is to set up a list of axioms, say wishes, that makes . look like a directional derivative. An optimal list of wishes would be such that one can fulfill these wishes but only in a unique way.

BET 发表于 2025-3-23 18:47:03

General Definition of Independent Random Variables and Laws of Large Numbers,The definition of independent real-valued random variables was given in Lecture 4. We now extend this definition to the case of more general random variables.

先兆 发表于 2025-3-23 22:45:40

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维持 发表于 2025-3-24 04:51:58

Riemann Surfaces,A . is a differentiable manifold with charts in . and holomorphic transition maps. In short, we can say that a Riemann surface is a surface with a .-structure.

dominant 发表于 2025-3-24 07:57:26

Conditional Probabilities and Expectations,Let (., ., .) be a probability space, . ∈ . and .(.) > 0. The conditional distribution on the set . is a probability distribution defined on the .—algebra . by ..

Inclement 发表于 2025-3-24 13:38:06

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Blazon 发表于 2025-3-24 18:08:00

Branching Processes,Here we consider another example of Markov chains, which arises in the analysis of so-called multiple decay processes for elementary particles. The theory of such processes was introduced in articles by the Soviet mathematicians A. N. Kolmogorov and B. A. Sevast’yanov.

Endoscope 发表于 2025-3-24 22:09:09

Markov Chains,The theory of Markov chains makes use of the theory of so-called stochastic matrices. We therefore begin with a small digression of a purely algebraic nature.

碎石 发表于 2025-3-25 01:02:35

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