PPT-Expectation And Variance of Random Variables Farrokh Alemi Ph.D.

Expectation And Variance of Random Variables Farrokh Alemi PhD Random Variable Probability of Random Variable Expected Value Expected Value Dental Service Dental Service Dental Service Dental Service. Let RS RS Find approximations for EG and Var using Taylor expansions of For any xy the bivariate 64257rst order Taylor expansion about is xy remainder Let EXEY The simplest approximation for XY is then XY The approximation for XY If is a random variable with this probability distribution 0 1 0 1 1 1 1 since the 0 term vanishes Let 1 and 1 Subbing 1 and 1 into the last sum and using the fact that the limits 1 and correspond to 0 and 1 respectively 0 1 1 1 1 0 RANDOM VARIABLES Definition usually denoted as X or Y or even Z and it is th e numerical outcome of a random process Example random process The number of heads in 10 tosses of a coin Example The number 5 rating CS648. . Lecture 4. Linearity of Expectation with applications. (Most important tool for analyzing randomized algorithms). 1. RECAP from the last lecture. 2. Random variable. Definition. :. . A random variable defined over a probability space (. 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.. Stern School of Business. IOMS Department . Department of Economics. Statistical Inference and Regression Analysis: . Stat-GB.3302.30, Stat-UB.0015.01. Part . 2 – A. Expectations of Random Variables. Defining Probability. Element. Event. Definition. Universe . of possibilities. Venn diagram. Definition. What is probability?. All possible events . What is probability?. All possible events . Event A. Chapter 5. : Limit Theorems. ENGG2430A Probability and Statistics for Engineers. Content. Markov and Chebyshev Inequalities. The Weak Law of Large Numbers. Convergence in Probability. The Central Limit Theorem. adding . constants to random variables, multiplying random variables by constants, and adding two random variables together. AP Statistics B. pp. 373-74. 1. Pp. 373-74 are just plain hard. I don’t like the way they are written. P(X=1) = P({3}) =1/6 X=5 P(X Let X = your earnings X = 100-1 = 99 X = -1 P(X=99) = 1/(12 3) = 1/220 P(X=-1) = 1-1/220 = 219/220 E(X) = 100*1/220 Let X be a random variable assuming the values x1, 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 provided that the sum is absolutely convergent. have a joint probability density function are finite. By induction, ], provided each expectation is finite. ][][1 7.3 Covariance, Variance of Sum PX1 P3 1/6 X5 PXLet X your earnings X 100-1 99 X -1 PX99 1/12 3 1/220 PX-1 1-1/220 219/220 EX 1001/220Let X be a random variable assuming the values x1 x2 x3 with corresponding probabi CHAPTER 4242MathematicalExpectationDefinition41IfXisarandomvariablethentheexpectedvalueforXisdefinedasNoteExpectedvalueofXmeanforXthefirstmomentforX3Definition42IfwisafunctionofXandtheprobabilityfunct