PPT-3.1 & 3.2: Fundamentals of Probability

Objective To understand and apply the basic probability rules and theorems CHS Statistics Inferential Statistics Recall Inferential statistics involve making predictions about a population . Mathematics 11 2 Probability and Statistics 3 Computational Tools 4 Et hics and Professional Practice 5 Engineering Economics 6 Statics 11 brPage 2br 7 Dynamics 8 Mecha nics of Materials 11 9 Materials 10 Fluid Mechanics 11 Hydraulics and Hydrologic Mathematics 12 2 Probability and Statistics 3 Engineering Sciences 4 Computational Tools 5 Materials Science brPage 2br 6 Chemistry 12 7 Fluid MechanicsDynamics 12 Thermodynamics 12 9 MaterialEnergy Balances 12 10 Heat Transfer 12 11 Mass Transfer a Stochastic Calculus: Introduction . Although . stochastic . and ordinary calculus share many common properties, there are fundamental differences. The probabilistic nature of stochastic processes distinguishes them from the deterministic functions associated with ordinary calculus. Since stochastic differential equations so frequently involve Brownian motion, second order terms in the Taylor series expansion of functions become important, in contrast to ordinary calculus where they can be ignored. . of a . Thriving Marriage. Selected Scriptures. ©. . November . 8, . 2015. Wade Harlan. ALL MARRIAGES TAKE WORK. Because there are usually big adjustments that must be . made . . .. as we discover more about our spouses.. ENGR 4323/5323. Digital and Analog Communication. Engineering and Physics. University of Central Oklahoma. Dr. Mohamed Bingabr. Chapter Outline. Concept of Probability. Random Variables. Statistical Averages (MEANS). 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. 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.. Slide . 2. Probability - Terminology. Events are the . number. of possible outcome of a phenomenon such as the roll of a die or a fillip of a coin.. “trials” are a coin flip or die roll. Slide . 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 . 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 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 .