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Probability: Difference between revisions
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Introductory Probability as taught in [https://www.pearson.com/us/higher-education/program/Ross-First-Course-in-Probability-A-9th-Edition/PGM110742.html Sheldon Ross' book] | Introductory Probability as taught in [https://www.pearson.com/us/higher-education/program/Ross-First-Course-in-Probability-A-9th-Edition/PGM110742.html Sheldon Ross' book] | ||
==Axioms of Probability== | |||
==Expectation and Variance== | |||
Some definitions and properties. | |||
===Total Expection=== | |||
Dr. Xu refers to this as the smooth property. | |||
<math>E(X) = E(E(X|Y))</math> | |||
{{hidden | Proof |}} | |||
===Total Variance=== | |||
This one is not used as often on tests as total expectation | |||
<math>Var(Y) = E(Var(Y|X)) + Var(E(Y | X)</math> | |||
{{hidden | Proof |}} | |||
==Delta Method== | |||
See [https://en.wikipedia.org/wiki/Delta_method Wikipedia] | |||
==Limit Theorems== | |||
===Markov's Inequality=== | |||
===Chebyshev's Inequality=== | |||
===Central Limit Theorem=== | |||
===Law of Large Numbers=== | |||
==Relationships between distributions== | ==Relationships between distributions== | ||