Distribution+Theory+-+Concepts

Distribution Theory (Concepts) (GWU EMSE-271)
Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts

1. What is the defintion of: a. PMF and PDF (==> EMSE 280 PDF and PMF) b. CDF (==> EMSE 280 CDF) 2. What is the definition of and rules for a. Expectation (==> EMSE 280 Expectation) b. Measues of Variance and Standard Deviation? (==> EMSE 280 Variance) 3. What is Covariance? a. What does positively and negatively dependence indicate? b. How is the covariance between two random variables defined? c. What determines if two rv's are uncorrelated? (covariance between two random variables) d. If rv's are uncorreletated, are they independent? (NO) 4. Discrete Univariate Models (Bernoulli, Binomial, Hyper geometric, Poisson, Geometric) (EMSE 271 - Slide 46) a. When can the Binomial Distribution be used to approximate the Hypergeomerticl Distribution? (EMSE 271 - Slide 52) b. When can the Poisson Distribution be used to approximate the Binominal Distribution? (EMSE 271 - Slide 52) c. When can the Normal Distribution be used to approximate the Binominal Distribution? (EMSE 271 - Slide 52) d. When can the Normal Distribution be used to appoximate the Poisson Distribution? (EMSE 271 - Slide 52) e. Under what conditions (what assumptions need to be true) to use each distribution? (EMSE 271 - Slide 52) 5. Continuous Univariate Models (Uniform, Exponential, Gamma, Normal, Beta, Wiebull) (EMSE 271 - Slide 47) a. Under what conditions (what assumptions need to be true) to use each distribution? (More a EMSE 280 question than 271?) -1- The normal versus the T-distribution? (When the sample size is large enough (30, 32, 50, 100 depending on the statistian.) 6. What are important properties of distribuitons (EMSE 280 viewpoint)? 7. What distributions are best used to solve what kind of problems? (Partial Start) a. Which distributions are commonly used for Hypothesis Testing for Means and Variances? b. In general?

8. What is a parametric family? a. What is the functional form (or kernal)? b. What is the constant of integration? c. How can the kernal and the constant be used to simplfy calculations to algebraic manipulations? (Weak) 9. How do you compute distirbution parameters?

10. See Homework 2, - Problems 2 for the kind of expectation and variance problems we might be expected to solve. - Problems 3 & 4 for the kind of distribution problems we might be expected to solve.