PPT-Random Variables

Expected Value Airline overbooking Pooling blood samples Variance and Standard Deviation Independent Collections Optimization DECS 430A Business Analytics I Class 2 Random Variables. Nimantha . Thushan. Baranasuriya. Girisha. . Durrel. De Silva. Rahul . Singhal. Karthik. . Yadati. Ziling. . Zhou. Outline. Random Walks. Markov Chains. Applications. 2SAT. 3SAT. Card Shuffling. Pieter . Abbeel. UC Berkeley EECS. Many slides adapted from . Thrun. , . Burgard. and Fox, Probabilistic Robotics. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . Value. Section . 7.4 (partially). Section Summary. Expected Value. Linearity of Expectations. Independent . Random . Variables. Expected Value. Definition. : The . expected value . (or . expectation . First center (expected value). Now - spread. 4.2 (cont.) Standard Deviation of a Discrete Random Variable. Measures how “spread out” the random variable is. Summarizing data and probability. Data. Careless assumptions of independence. Covariance . and . correlation. Spreadsheet tools for optimization (Solver). The Central Limit Theorem and. the normal distribution. Business . Analytics . I. Session 3. 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.. 1. Matt Gormley. Lecture 2. August 31, 2016. School of Computer Science. Readings:. Mitchell Ch. 1, 2, 6.1 – 6.3. Murphy Ch. 2. Bishop Ch. 1 - 2. 10-601 Introduction to Machine Learning. Reminders. 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. 1. 5. Joint Probability Distributions. 5-1 Two or More Random Variables. 5-1.1 Joint Probability Distributions. 5-1.2 Marginal Probability Distributions. 5-1.3 Conditional Probability Distributions. class is part of the . java.util. package. It provides methods that generate pseudorandom numbers. A . Random. object performs complicated calculations based on a . seed value. to produce a stream of seemingly random values. 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, 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 Covariance . and . correlation. Spreadsheet tools for optimization (Solver). The Central Limit Theorem and. the normal distribution. Business . Analytics . I. Session 3. Predicting the Results of the . Section 6.1. Discrete and Continuous. Random Variables. Discrete and Continuous Random Variables. USE the probability distribution of a discrete random variable to CALCULATE the probability of an event..