PPT-Chapter 5. Continuous Probability Distributions

Section 56 Normal Distributions Jiaping Wang Department of Mathematical Science 03272013 Wednesday Outline Probability Density Function Mean and Variance More Examples Homework 9. Probability Distributions . and Data Modeling. Business Analytics: Methods, Models, . and Decisions. , 1. st. edition. James R. Evans. 5-. 1. Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall. 1. 4. Continuous Random Variables and Probability Distributions. 4-1 Continuous Random Variables. 4-2 Probability Distributions and Probability Density Functions. 4-3 Cumulative Distribution Functions. 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. 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 . Continuous distributions. Sample size 24. Guess the mean and standard deviation. Dot plot sample size 49. Draw the population distribution you expect. Sample size 93. Sample size 476. Sample size 948. 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. Normal Distribution. Log Normal Distribution. Gamma Distribution. Chi Square Distribution. F Distribution. t Distribution. Weibull Distribution. Extreme Value Distribution (Type I and II. ). Exponential. 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.. . 4.1 - . Probability Density Functions. 4.2 - Cumulative Distribution . Func. tions. and. . . . Expected Values. . . 4.3 - The Normal Distribution. . 4.4 - . The Exponential and Gamma Distributions. John Hancock Financial Services. What Is An Actuary?. “Actuaries are highly sought-after professionals who develop and communicate solutions for complex financial issues.”. What Do Actuaries Do?. 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 . Continuous Probability Distribution . (pdf) . Definition:. . b. P(a . . X.  . b) = .  . f(x). dx. . . a. For continuous RV X & a. .  b.. 3. Four Mini-Lectures . QMM 510. Fall . 2014 . 7-. 2. Continuous Probability Distributions . ML 5.1. . Chapter Contents. 7.1 Describing a Continuous Distribution. 7.2 Uniform Continuous Distribution . How . can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects . of reality. Albert Einstein. Some parts of these slides were prepared based on .