week3 - = Permutation x n n P x n − = Some Distributions...

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Econ 41, Fall 2006 TA: Ruo Chen Week 3 (Oct 18 th , 2006) Probability Basic Concepts Three approaches to define probability Classical approach Frequentist approach Subjective approach Marginal probability: P(A), P(B) Conditional probability: P(A|B), P(B|A) Mutually exclusive events: A and B = Φ Independent events: P(A|B)=P(A) or P(B|A)=P(B) Complementary events: A includes all outcomes that not in A. Intersection of events: A and B, or A B Union of events: A or B, or A ∪B General Rules 1) Relation between mutually exclusive events and independent events z Mutually exclusive => dependent z Independent => not mutually exclusive 2) Relation among events z ) ( ) ( ) | ( B P B and A P B A P = z ) ( ) | ( ) ( ) | ( ) ( A P A B P B P B A P B and A P = = z ) ( ) ( ) ( ) ( B and A P B P A P B or A P + = 3) Independent events z ) ( ) | ( A P B A P = z ) ( ) | ( B P A B P = z ) ( ) ( ) ( B P A P B and A P = 4) Mutually exclusive events z 0 ) ( = B and A P
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z ) ( ) ( ) ( B P A P B or A P + = Discrete Random Variables and Probability Distribution Basic Concepts Probability distribution Mean Standard deviation Factorial: n! Combination: )! ( ! ! x n x n C x n
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Unformatted text preview: = Permutation: )! ( ! x n n P x n − = Some Distributions Bernoulli distribution Binomial distribution Negative binomial distribution Poisson distribution Hypergeometric distribution Discrete uniform distribution Probability ) ( x P ⎩ ⎨ ⎧ = − = 1 1 x if p x if p x n x x n p p C − − ) 1 ( r x r r x p p C − − − − ) 1 ( 1 1 ! x e x λ − n N x n r N x r C C C − − m 1 Description The probability of certain outcome (x=1, “pass”; x=0, “fail”) The probability of exactly x “pass” in the n trials. The probability of x trials that derive r “pass” with the last one is “pass”. The probability of x occurrences in an interval The probability of x success in n trials The probability of outcome x. (total m outcomes) Mean p np 2 1 + m Standard Devistion ) 1 ( p p − ) 1 ( p np − 12 1 2 − m...
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week3 - = Permutation x n n P x n − = Some Distributions...

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