| Line 10: | Line 10: | ||
'''Definition of conditional probability, and properties thereof''' | '''Definition of conditional probability, and properties thereof''' | ||
| − | <math>P(A|B) = \frac{P(A \ | + | <math>P(A|B) = \frac{P(A \cap B)}{P(B)}</math> |
Propertie: | Propertie: | ||
| − | 1) <math>P(A|B) \ge 0 | + | 1) <math>P(A|B) \ge 0</math> |
| − | 2) <math>P( \Omega |B) >= 0 | + | 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>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 16:43, 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 \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
