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Probability: Difference between revisions
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Calculus-based Probability | |||
==Axioms of Probability== | ==Axioms of Probability== | ||
* <math>0 \leq P(E) \leq 1</math> | * <math>0 \leq P(E) \leq 1</math> | ||
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<math>Var(Y) = E(Var(Y|X)) + Var(E(Y | X)</math> | <math>Var(Y) = E(Var(Y|X)) + Var(E(Y | X)</math> | ||
{{hidden | Proof |}} | {{hidden | Proof |}} | ||
==Convergence== | |||
There are 4 types of convergence typically taught in undergraduate courses.<br> | |||
See [https://en.wikipedia.org/wiki/Convergence_of_random_variables Wikipedia Convergence of random variables] | |||
===Almost Surely=== | |||
===In Probability=== | |||
* Implies Convergence in distribution | |||
===In Distribution=== | |||
* Equivalent to convergence in probability if it converges to a degenerate distribution | |||
===In Mean Squared=== | |||
==Delta Method== | ==Delta Method== | ||
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Too many. See [https://en.wikipedia.org/wiki/F-distribution the Wikipedia Page]. | Too many. See [https://en.wikipedia.org/wiki/F-distribution the Wikipedia Page]. | ||
Most important are Chi-sq and T distribution | Most important are Chi-sq and T distribution | ||
==Textbooks== | |||
* Sheldon Ross' A First Course in Probability | |||
* [https://smile.amazon.com/Introduction-Mathematical-Statistics-Robert-Hogg/dp/0321795431?sa-no-redirect=1 Hogg and Craig's Mathematical Statistics] | |||
* Casella and Burger's Statistical Inference | |||