Random Variables. an important concept in probability. A random variable , X, is a numerical quantity whose value is determined be a random experiment. Examples Two dice are rolled and X is the sum of the two upward faces.

ByIntroduction to R. Summer session: Lecture 3 Brian Healy. Outline. Discussion of R Importing and changing data Creating your own data Summary statistics / graphs Tests for normality. What is R?. Statistical computer language similar to S-plus Has many built-in statistical functions

ByOutline: Independence. Odds ratios. Random variables. Distribution function, pmf, density. Expected value . Independence: P(B | A) = P(B) (and vice versa) [so, when independent, P(A&B) = P(A)P(B|A) = P(A)P(B).] Reasonable to assume the following are independent:

ByUse of moment generating functions . Definition. Let X denote a random variable with probability density function f ( x ) if continuous (probability mass function p ( x ) if discrete) Then m X ( t ) = the moment generating function of X.

ByThe Monte Carlo Method: an Introduction. Detlev Reiter. Research Centre Jülich (FZJ) D -52425 Jülich http://www.fz-juelich.de e-mail: d.reiter@fz-juelich.de Tel.: 02461 / 61-5841. Vorlesung HHU Düsseldorf , WS 07/08 March 2008. There are two dominant methods of simulation

ByOperational vulnerability indicators. Anand Patwardhan IIT-Bombay. Context and objectives matter. Vulnerability. A composite measure of the sensitivity of the system and its adaptive (coping) capacity Combine hazard, exposure and response layers

ByMath 10 Chapter 6 Notes: The Normal Distribution. Notation: X is a continuous random variable X ~ N( , ) Parameters: is the mean and is the standard deviation Graph is bell-shaped and symmetrical The mean, median, and mode are the same (in theory).

ByContinuous Random Variables. Continuous Random Variable. A continuous random variable is one for which the outcome can be any value in an interval of the real number line. Usually a measurement. Examples Let Y = length in mm Let Y = time in seconds Let Y = temperature in ºC.

ByReview of Basic Probability and Statistics. ISE525: Spring 10. Random Variables and Their Properties. Experiment : a process whose outcome is not known with certainty. Set of all possible outcomes of an experiment is the sample space. Outcomes are sample points in the sample space.

ByDiversity techniques for flat fading channels. BER vs. SNR in a flat fading channel Different kinds of diversity techniques Selection diversity performance Maximum Ratio Combining performance. BER vs. SNR in a flat fading channel. Proakis, 3rd Ed. 14-3.

BySimulating Normal Random Variables. Simulation can provide a great deal of information about the behavior of a random variable. Simulating Normal Random Variables. Two types of simulations (1) Generating fixed values - Uses Random Number Generation (2) Generating changeable values

ByIn the Name of the Most High . Continuous Random Variables and Reliability Analysis. Behzad Akbari Spring 2009 Tarbiat Modares University. These slides are based on the slides of Prof. K.S. Trivedi (Duke University). Definitions. Distribution function:

ByMarking to Market: Panacea or Pandora’s Box?. Guillaume Plantin Haresh Sapra Hyun Song Shin. Case for Marking to Market. Market price reflects current terms of trade between willing parties Market price gives better indication of current risk profile Market discipline

ByCellular COMMUNICATIONS. LTE. Data Rate. Requirements And Targets to LTE. reduced delays, in terms of both connection establishment and transmission latency; increased user data rates; increased cell-edge bit-rate, for uniformity of service provision;

ByChapter 2. Random Variables. 2.1 Discrete Random Variables 2.2 Continuous Random Variables 2.3 The Expectation of a Random Variable 2.4 The Variance of a Random Variable 2.5 Jointly Distributed Random Variables 2.6 Combinations and Functions of Random Variables. -3. -2. -1. 1. 0. 2. 3.

ByExploratory Analysis of Survey Data. Lisa Cannon Luke Peterson. Presentation Outline. Density Estimation Nonparametric kernel density estimates Properties of kernel density estimators Other methods Graphical Displays NHANES data. Three features that distinguish survey data:.

By“Good Practices” for long term orbit propagation and associated criteria verification in the frame of the French Space Act. Hubert.Fraysse@cnes.fr. Presentation to ISO – Berlin - May 24 th 2011. Summary. 1. French Space Act : disposal orbits relatively to region A and B

ByChapter 3. Discrete Probability Distributions. 3.1 The Binomial Distribution 3.2 The Geometric and Negative Binomial Distributions 3.3 The Hypergeometric Distribution 3.4 The Poisson Distribution 3.5 The Multinomial Distribution.

BySTAT3600. Lecture 5 Chapter III Discrete Random Variables and Probability Distributions. Discrete Random Variables.

ByPrimer on Statistics for Interventional Cardiologists Giuseppe Sangiorgi, MD Pierfrancesco Agostoni, MD Giuseppe Biondi-Zoccai, MD. What you will learn. Introduction Basics Descriptive statistics Probability distributions Inferential statistics Finding differences in mean between two groups

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