PPT-Theorem of total probability

Let B 1 B 2 B N be mutually exclusive events whose union equals the sample space S We refer to these sets as a partition of S An event A can be represented as Since B 1 B 2. Continued Fractions. Lisa Lorentzen. Norwegian University of Science and Technology. Continued fraction:. Convergence:. Möbius. transformations:. Convergence:. Catch:. L (1986). General convergence:. Independent Events. Events can be "Independent", meaning each event is . not affected. by any other events.. Example: Tossing a coin.. Each toss of a coin is a perfect isolated thing. . What it did in the past will not affect the current toss.. Theorem. Common fallacies of probability:. The . Gambler’s . Fallacy. Is assuming that the odds of a single truly random event are affected in any way by previous iterations of the same or other truly random event. 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). 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.. Conditional Probability. Conditional Probability: . A probability where a certain prerequisite condition has already been met.. Conditional Probability Notation. The probability of Event A, given that Event B has already occurred, is expressed as P(A | B).. 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 . Chapter Summary. Introduction to Discrete Probability. Probability Theory. Bayes. ’ Theorem. An Introduction to Discrete Probability. Section . 7.1. Section Summary. Finite Probability. Probabilities of Complements and Unions of Events. Probability Theory Section Summary Assigning Probabilities Probabilities of Complements and Unions of Events Conditional Probability Independence Random Variables Assigning Probabilities Let S be a sample space of an experiment with a finite number of outcomes. We assign a probability 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 CS201 – Bayes ’ Theorem – Excerpts http://en.wikipedia.org/wiki/Bayes%27_theorem http://en.wikipedia.org/wiki/Bayesian_infere nce Bayes's theorem is stated mathematically as the following sim It is also known as the Gaussian distribution and the bell curve. .. The general form of its probability density function is-. Normal Distribution in . Statistics. The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. .