Exam 2 - Probability

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Department
Statistics and Probability
Course Code
STT 201
Professor
Prof.Pathak

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STT 201 Notes for Exam 2 Axiomatic Probability 1/30/13 - 2/25/13 FOUNDERS:  A.N. Kolmogorov  S.R.S. Varadhan TOTAL PROBABILITY:  Sample Space (S) = {all possible outcomes}  Events (E) = {outcomes you want} o Null: Nothing happens and P=0 o Sure: Everything happens and P=1  Probability (P): o (P) = where n=number of repetitions  Use nPr for exact number  Use nCr for at most o Multiple Trials:  F = Failures  S = Successes  (P(F)) (P(S))S o Complementation Rule: Finds the probability of at least one desired event happening  P(A )=1-P(A)  Conditional Probability: Probability of events are dependent on each other ( ) ( ) ( |) o P(A|B) = ( ) ( ) o Multiplication Rule:  P(A and B) = P(A)*P(B|A) o Addition Rule:  P(A or B) = P(A) + P(B) – P(A and B)  Unconditional Probability: Weighted average of conditional probabilities o P = ∑ o Independence:  P(A and B) = P(A)*P(B) BINOMIAL PROBABILITY: Binomial Distributions: Distribution of number “x” of successes in “n” independent trials of an experiment with a constant probability “p” of success (AKA a bell curve)  Notation: o Mean = µ
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