PPT-Introduction to Probability

and Statistics Chapter 5 Discrete Distributions Discrete Random Variables Discrete random variables take on only a finite or countable many of values Number of heads in 1000 trials of coin tossing. Assigning Probabilities and Probability Relationships. Chapter 4. BA 201. Assigning Probabilities. Assigning Probabilities. Basic Requirements for Assigning Probabilities. 1. The probability assigned to each experimental. Jake Blanchard. Spring 2010. Uncertainty Analysis for Engineers. 1. Introduction. Interpretations of Probability. Classical – If an event can occur in N equally likely and different ways, and if n of these have an attribute A, then the probability of the occurrence of A, denoted Pr(A), is defined as n/N. Experimental probability. : . Probability based on a collection of data.. Will have a table of results or data from the experiment(s)!. What is the difference between . theoretical probability. and . Coins game. Toss 3 coins. You win if . at least two . come out heads. S. = { . HHH. , . HHT. , . HTH. , . HTT. , . T. HH. , . T. HT. , . T. TH. , . T. TT. }. equally likely outcomes. W. = { . HHH. Random Variables. Definition:. A rule that assigns one (and only one) numerical value to each simple event of an experiment; or. A function that assigns numerical values to the possible outcomes of an experiment.. 3.1 . The Concept of Probability. 3.2 . Sample Spaces and Events. 3.3 . Some Elementary Probability Rules. 3.4 . Conditional Probability and Independence. 3.5 . Bayes’ Theorem. 3-. 2. Probability Concepts. 4. Introduction. (slide 1 of 3). A key . aspect of solving real business problems is dealing appropriately with uncertainty.. This involves recognizing explicitly that uncertainty exists and using quantitative methods to model uncertainty.. What we learned last class…. We are not good at recognizing/dealing with randomness. Our “random” coin flip results weren’t streaky enough.. If B/G results behave like independent coin flips, we know how many families to EXPECT with 0,1,2,3,4 girls.. Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . Introduction to Probability and Statistics Chapter 5 Discrete Distributions Discrete Random Variables Discrete random variables take on only a finite or countable many of values . Number of heads in 1000 trials of coin tossing Probability and Probability Distribution Dr Manoj Kumar Bhambu GCCBA-42, Chandigarh M- +91-988-823-7733 mkbhambu@hotmail.com Probability and Probability Distribution: Definitions- Probability Rules –Application of Probability What is probability?. Classical definition:. the . ratio. of “favorable” to equally probable . cases. .. “. favorable”. :. . the kind you’re interested . in. .. Probability of getting heads on flipping a fair coin: 1/2 (heads is 1 of 2 possibilities). calculus. 1 ≥ . Pr. (h) ≥ 0. If e deductively implies h, then Pr(h|e) = 1. .. (disjunction rule) If h and g are mutually exclusive, then . Pr. (h or g) = . Pr. (h) + . Pr. (g). (disjunction rule) If h and g are . 4. Compute the number of combinations of . n. individuals taken . k. at a time.. Use . combinations to calculate probabilities.. Use . the multiplication counting principle and combinations to calculate probabilities..