PPT-Discrete Probability Distributions

Unit 4 Introduction Many decisions in business insurance and other reallife situations are made by assigning probabilities to all possible outcomes pertaining to the situation and then evaluating the results For example a saleswomen can compute the probability that she will make 012 or 3 or more sales in a single day An insurance company might be able to assign probabilities to the number of vehicles a family owns Once these probabilities are assigned statistics such as mean variance and standard deviations can be computed for these events With these statistics various decisions can be made. AS91586 Apply probability distributions in solving problems. NZC level 8. Investigate situations that involve elements of chance. calculating and interpreting expected values and standard deviations of discrete random variables. Dr. Feng Gu. Way to study a system. . Cited from Simulation, Modeling & Analysis (3/e) by Law and . Kelton. , 2000, p. 4, Figure 1.1. Model taxonomy. Modeling formalisms and their simulators . Discrete time model and their simulators . A Brief Introduction. Random Variables. Random Variable (RV): A numeric outcome that results from an experiment. For each element of an experiment’s sample space, the random variable can take on exactly one value. 1. http://www.landers.co.uk/statistics-cartoons/. 5.1-5.2: Random Variables - Goals. Be able to define what a random variable is.. Be able to differentiate between discrete and continuous random variables.. Applied Statistics and Probability for Engineers. Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 5 Title and Outline. 2. 5. Joint Probability Distributions. 5-1 Two or More Random Variables. 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.. St. . Edward’s. University. .. .. .. .. .. .. .. .. .. .. .. Chapter 5. Discrete Probability Distributions. .10. .20. .30. .40. 0 . . 1 . . 2 3 4. Random Variables. 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.. Section 5-3 – Normal Distributions: Finding Values. A. We have learned how to calculate the probability given an . x. -value or a . z. -score. . In this lesson, we will explore how to find an . Fall 2010. Sukumar Ghosh. Sample Space. DEFINITION. . The . sample space S . of an experiment is the set . of possible outcomes. An . event. . E. is a . subset. of the sample space.. What is probability?. II. BINOMIAL DISTRIBUTIONS A. Binomial Experiments 1. A binomial experiment is a probability experiment that satisfies the following conditions: a. The experiment is repeated for a fixed number of independent trials. Probability Space of Two Die. σ-. Algebra (. ℱ. ). Sample Space (Ω). [...]. E5={(1,4),(2,3),(3,2),(4,1)}. [...]. Probability Measure Function (P). P. E5. 0.11. Probability Measure Function (P). . 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 Nisheeth. Random Variables. 2. Informally, a random variable (. r.v.. ) . denotes possible outcomes of an event. Can be discrete (i.e., finite many possible outcomes) or continuous. Some examples of discrete .