PPT-Continuous Probability Distributions

Chapter 7 Learning Objectives LO7 2 Describe the characteristics of a normal probability distribution LO73 Describe the standard normal probability distribution and use it to calculate probabilities. 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. Distributions. 6.1 Continuous Uniform Distribution. One of the simplest continuous distributions in all of statistics is the . continuous. uniform distribution. . This distribution is characterized by a density function. 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?. Continuous Probability Distribution . (pdf) . Definition:. . b. P(a . . X.  . b) = .  . f(x). dx. . . a. For continuous RV X & a. .  b.. 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. 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 . 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). .