tailieunhanh - Lecture Probability & statistics: Chapter 4 - Bùi Dương Hải

Lecture "Probability & statistics - Chapter 4: Basic probability" has contents: Probability, outcome – event complement event, intersection event, union event mutually exclusive, independent, collectively exhausive, partitions bernoulli formula total probability, bayes’ theorem. | Lecture Probability & statistics: Chapter 4 - Bùi Dương Hải Lecture 4. BASIC PROBABILITY Probability Outcome – Event Complement Event, Intersection Event, Union Event Mutually Exclusive, Independent, Collectively Exhausive, Partitions Bernoulli Formula Total Probability, Bayes’ Theorem [1] Chapter 4, pp. 169 - 212 PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 1 “Problem of Points” 2 players A and B, contributed 50 Franc each. The game is winner – loser only (no draw), A and B are equally-likely to win in each match. Game rule: play 9 matches, the one wins more is final winner and takes all of 100F But the game had stopped after 7 matches, and scores at that time of A and B are 4 and 3, respectively. How could they distribute the money? PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 2 . Probability Probability is quantitative measure of uncertainty, the chance that an uncertain event will occur. Probability: Subjective and Objective Probability of event A is denoted by P(A) 0 ≤ P(event) ≤ 1 P(always) = 1 P(impossible) = 0 ( ) > ( ): A is more possible to occur than B PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 3 Experiment – Outcome - Event Experiment Outcome Event Flip a coin Head, tail ‘Head’, ‘tail’ Toss a die 1,2,3,4,5,6 dot(s) ‘greater than 3’ Do an exam Score = 0, 1, 2, , 10 ‘pass’; ‘excellent’ Invest in a project Profit: (+), (–), zero ‘Non negative’ ‘profitable’ Apply for a job Pass, fail Do a job Salary = PROBABILITY & STATISTICS– Bui Duong Hai – NEU – 4 Classical Probability Sample space: all basic outcomes, denoted by Ω Assumes all basic outcomes in the sample space are equally-likely to occur Number of basic outcomes: Number of basic outcomes for event A: Probability of event .