PPT-Introduction to Probability

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. T.Jagannadha. . Swamy. Dept of . ECE,Griet. Random Variable. A random variable . x. takes on a defined set of values with different probabilities.. For example, if you roll a die, the outcome is random (not fixed) and there are 6 possible outcomes, each of which occur with probability one-sixth. . QSCI 381 – Lecture 12. (Larson and Farber, Sect 4.1). Learning objectives. Become comfortable with variable definitions. Create and use probability distributions. Random Variables-I. A . 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. 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. 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 . Probability Terminology. Classical Interpretation. : Notion of probability based on equal likelihood of individual possibilities (coin toss has 1/2 chance of Heads, card draw has 4/52 chance of an Ace). Origins in games of chance.. AMATYC Presentation November 2009. Lance Phillips – Tulsa Community College. The Vocabulary of Probability. Experiment – A situation which involves chance or probability the result of which is called an outcome.. 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 . A value between zero and one that describe the relative possibility(change or likelihood) an event occurs.. The MEF announces that in 2012 the change Cambodia economic growth rate is equal to 7% is 80%.. 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). 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.. 4. Interpret probability as a long-run relative frequency. . Dispel . common myths about randomness.. Use . simulation to model chance behavior.. Randomness, Probability, and Simulation. Randomness, Probability, and Simulation.