18_05_lec1

18_05_lec1 - 18.05 Spring 2005 Lecture Notes 18.05 Lecture...

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18.05 Spring 2005 Lecture Notes 18.05 Lecture 1 February 2, 2005 Required Textbook - DeGroot Schervish, “Probability and Statistics,” Third Edition Recommended Introduction to Probability Text - Feller, Vol. 1 § 1.2-1.4. Probability, Set Operations. What is probability? Classical Interpretation: all outcomes have equal probability (coin, dice) Subjective Interpretation (nature of problem): uses a model, randomness involved (such as weather) ex. drop of paint falls into a glass of water, model can describe P (hit bottom before sides) or, P (survival after surgery)- “subjective,” estimated by the doctor. Frequency Interpretation: probability based on history P (make a free shot) is based on history of shots made. Experiment has a random outcome. 1. Sample Space - set of all possible outcomes. coin: S= { H, T } , die: S= { 1, 2, 3, 4, 5, 6 } two dice: S= { (i, j), i, j=1, 2, ..., 6 } 2. Events - any subset of sample space ex. A S, A - collection of all
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18_05_lec1 - 18.05 Spring 2005 Lecture Notes 18.05 Lecture...

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