Review_of_Probability_and_Probability_Di[1]

# Review_of_Probabilit - Stat 231 Ch.1 1 Data Analysis(Chapter 1 Probability and Probability Distributions(Review from Stat 230 Probability Axioms

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S t a t 2 3 1 - C h . 1 1 Data Analysis (Chapter 1) Probability and Probability Distributions (Review from Stat 230) Probability Axioms : P( S ) = 1, where S is the sample space P( ) = 0, where is the null set P(A B) = P(A) + P(B) whenever A B = Basic Rules of Probability : P(A B) = P(A) + P(B) - P(A B) P(A|B) = PAB PB () ( conditional probability) Events A, B are independent iff P(A B) = P(A)P(B)

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S t a t 2 3 1 - C h . 1 2 Random Variables and Probability Functions : A random variable is a function which assigns a real number to each point in a sample space (or, more informally, a number whose value is determined ‘by chance’) Types of Random Variables : Discrete random variables take on only countable (esp. integer) values (e.g., number of people in a class, grade in a course, age (years)) Continuous random variables take on all values over one or more intervals of the real line (e.g., height, weight, time) For a discrete r.v. Y, the probability (mass) function ) ( y f Y is defined as ) ( ) ( y Y P y f Y = = For a continuous r.v. Y, the
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## This note was uploaded on 04/18/2010 for the course STAT 231 taught by Professor Cantremember during the Spring '08 term at Waterloo.

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Review_of_Probabilit - Stat 231 Ch.1 1 Data Analysis(Chapter 1 Probability and Probability Distributions(Review from Stat 230 Probability Axioms

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