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'''Definition of conditional probability, and properties thereof'''
 
'''Definition of conditional probability, and properties thereof'''
  
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<math>P(A|B) = \frac{P(A \cap B)}{P(B)}</math>
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Propertie:
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1) <math>P(A|B) \ge 0}</math>
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2) <math>P(\Omega|B) >= 0}</math>
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3) if A1 and A2 are disjoint
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  <math>P(A1\cupA2|B) = P(A1|B) + P(A2|B)}</math>
  
 
'''Bayes rule and total probability'''
 
'''Bayes rule and total probability'''

Revision as of 17:39, 23 September 2008

You can get/put ideas for what should be on the cheat sheet here. DO NOT SIGN YOUR NAME

Sample Space, Axioms of probability (finite spaces, infinite spaces)

$ P(A) \geq 0 $ for all events A

Properties of Probability laws


Definition of conditional probability, and properties thereof

$ P(A|B) = \frac{P(A \cap B)}{P(B)} $ Propertie: 1) $ P(A|B) \ge 0} $ 2) $ P(\Omega|B) >= 0} $ 3) if A1 and A2 are disjoint

  $ P(A1\cupA2|B) = P(A1|B) + P(A2|B)} $

Bayes rule and total probability

$ P(A|B) = \frac{P(A \cap B)}{P(B)} $

Definitions of Independence and Conditional independence


Definition and basic concepts of random variables, PMFs


The common random variables: bernoulli, binomial, geometric, and how they come about in problems. ALSo their PMFs.

Geometric RV

P(X=k) = (1-p)^(k-1) * p for k>=1

$ E[X] = 1/p $


Definition of expectation and variance and their properties

$ Var(X) = E[X^2] - (E[X])^2 $


Joint PMFs of more than one random variable

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To all math majors: "Mathematics is a wonderfully rich subject."

Dr. Paul Garrett