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

Revision as of 17:43, 23 September 2008

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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 \cup A2|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

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett