PPT-Theorem of total probability

Author : zoe | Published Date : 2023-05-27

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

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Theorem of total probability: Transcript


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. Let IR be a continuous function and IR IN be a sequence of continuous functions If IN converges pointwise to and if 1 for all and all IN then IN converges uniformly to Proof Set for each IN Then IN is a sequence of continuous functions on the co Then there exists a number in ab such that The idea behind the Intermediate Value Theorem is When we have two points af and bf connected by a continuous curve The curve is the function which is Continuous on the interval ab and is a numb 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. 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 . 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 . 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. 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 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 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 . Random variable: A variable whose value is determined by the outcome of a random experiment is called a random variable. Random variable is usually denoted by X. A random variable may be discrete or 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.

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