Lecture 6: Discrete Random Variables
Lecture 6: Discrete Random Variables 19 September 2005 1 Expectation The expectation of a random variable is its average value, with weights in the average given by the probability distribution E[X] = X x Pr(X = x)x If c is a constant, E[c] = c. …
Download Lecture 6: Discrete Random Variables
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
Advertisement
Documents from same domain
Chapter 14 Within-Subjects Designs - CMU Statistics
www.stat.cmu.eduChapter 14 Within-Subjects Designs ... although often the term repeated measures analysis is used in a narrower sense to indicate the speci c set of analyses discussed
Analysis, Design, Chapter, Subject, Measure, Within, Repeated, Repeated measures analysis, Chapter 14 within subjects designs
Chapter 9 Simple Linear Regression
www.stat.cmu.eduChapter 9 Simple Linear Regression An analysis appropriate for a quantitative outcome and a single quantitative ex-planatory variable. 9.1 …
Linear, Chapter, Simple, Regression, Chapter 9 simple linear regression
Lecture Notes 9 Asymptotic Theory (Chapter 9)
www.stat.cmu.eduLecture Notes 9 Asymptotic Theory (Chapter 9) In these notes we look at the large sample properties of estimators, especially the maxi-mum likelihood estimator.
2 Probability Theory and Classical Statistics
www.stat.cmu.edu2 Probability Theory and Classical Statistics Statistical inference rests on probability theory, and so an in-depth under-standing of the basics of probability theory is necessary for acquiring a con-
Statistics, Theory, Probability, Classical, Probability theory, Probability theory and classical statistics
Ryan Tibshirani Data Mining: 36-462/36-662 January 22 2013
www.stat.cmu.eduRyan Tibshirani Data Mining: 36-462/36-662 January 22 2013 Optional reading: ESL 14.10 1. Information retrieval with the web Last time:information retrieval, learned how to compute similarity scores (distances) of documents to a given query string But what if …
Data, Mining, Yarn, Tibshirani, Ryan tibshirani data mining, 36 462
Ryan Tibshirani Data Mining: 36-462/36-662 April 25 2013
www.stat.cmu.eduBoosting Boosting1 is similar to bagging in that we combine the results of several classi cation trees. However, boosting does something fundamentally di erent, and can work a lot better As usual, we start with training data (x
Data, Mining, Yarn, Tibshirani, Ryan tibshirani data mining, 36 462
Chapter 8 Threats to Your Experiment - CMU Statistics
www.stat.cmu.eduThis chapter discusses possible complaints about internal validity, external validity, construct validity, Type 1 error, and power. We are using \threats" to mean things that will reduce the impact of
Your, Internal, Threats, Experiment, External, Validity, External validity, Internal validity, 8 threats to your experiment
Advanced Data Analysis from an Elementary Point of View
www.stat.cmu.eduAdvanced Data Analysis from an Elementary Point of View Cosma Rohilla Shalizi
Finding Informative Features - CMU Statistics
www.stat.cmu.eduSimilarly, our uncertainty about the class C, in the absence of any other information, is just the entropy of C: H[C] = X c Pr(C= c)log 2 Pr(C= c) Now suppose we observe the value of the feature X.
Feature, Findings, Class, Informative, Class c, Finding informative features
Degrees of Freedom and Model Search - CMU Statistics
www.stat.cmu.eduDegrees of Freedom and Model Search Ryan J. Tibshirani Abstract Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quan-titative description of the amount of tting performed by a given procedure. But, despite this
Model, Degree, Search, Freedom, Degrees of freedom and model search
Related documents
Expected Value The expected value of a random variable ...
www.columbia.eduEx. An indicator variable for the event A is defined as the random variable that takes on the value 1 when event A happens and 0 otherwise. I A = 1 if A occurs C 0 if Aoccurs P(I A =1) C= P(A) and P(I A =0) = P(A) The expectation of this indicator (noted I A) is E(I A)=1*P(A) + 0*P(AC) =P(A). One-to-one correspondence between expectations and ...
Chapter 6 - Random Processes
www.ece.uah.eduContinuous and Discrete Random Processes For a continuous random process, probabilistic variable takes on a continuum of values. For every fixed value t = t0 of time, X(t0; ) is a continuous random variable. Example 6-2: Let random variable A be uniform in [0, 1]. Define the continuous random
POL 571: Convergence of Random Variables
imai.fas.harvard.edumodel (i.e., a random variable and its distribution) to describe the data generating process. What we observe, then, is a particular realization (or a set of realizations) of this random variable. The goal of statistical inference is to figure out the true probability model given the data you have.
POL571 Lecture Notes: Expectation and Functions of Random ...
imai.fas.harvard.edu8. Cauchy distribution. A Cauchy random variable takes a value in (−∞,∞) with the fol-lowing symmetric and bell-shaped density function. f(x) = 1 π[1+(x−µ)2]. The expectation of Bernoulli random variable implies that since an indicator function of a random variable is a Bernoulli random variable, its expectation equals the probability.
18.440: Lecture 18 Uniform random variables
ocw.mit.eduR R R R Properties of uniform random variable on [0, 1] Suppose X is a random variable with probability density 1 x ∈ [0, 1] function f (x) =
Two Proofs of the Central Limit Theorem
www.cs.toronto.eduA Bernoulli random variable Ber(p) is 1 with probability pand 0 otherwise. A binomial random variable Bin(n;p) is the sum of nindependent Ber(p) variables. Let us nd the moment generating functions of Ber(p) and Bin(n;p). For a Bernoulli random variable, it is very simple: M Ber(p) = (1 p) + pe t= 1 + (et 1)p:
Notes on the Poisson and exponential distributions
www.kellogg.northwestern.eduA continuous random variable is a random variable which can take any value in some interval. A continuous random variable is characterized by its probability density function, a graph which has a total area of 1 beneath it: The probability of the random variable taking values in any interval is simply the ...
Chapter 3 Continuous Random Variables
www.pnw.eduRandom variable Xis continuous if probability density function (pdf) fis continuous at all but a nite number of points and possesses the following properties: f(x) 0, for all x, R 1 1 f(x) dx= 1, P(a<X b) = R b a f(x) dx The (cumulative) distribution function (cdf) for random variable Xis F(x) = P(X x) = Z x 1 f(t) dt; and has properties lim x ...