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Solutions for Chapter 3: Distributions of Random Variables

OpenIntro Statistics | 3rd Edition | ISBN: 9781943450039 | Authors: David M Diez; Christopher D Barr; Mine Çetinkaya-Rundel

Full solutions for OpenIntro Statistics | 3rd Edition

ISBN: 9781943450039

OpenIntro Statistics | 3rd Edition | ISBN: 9781943450039 | Authors: David M Diez; Christopher D Barr; Mine Çetinkaya-Rundel

Solutions for Chapter 3: Distributions of Random Variables

Solutions for Chapter 3
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Textbook: OpenIntro Statistics
Edition: 3
Author: David M Diez; Christopher D Barr; Mine Çetinkaya-Rundel
ISBN: 9781943450039

Since 44 problems in chapter 3: Distributions of Random Variables have been answered, more than 41303 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3: Distributions of Random Variables includes 44 full step-by-step solutions. OpenIntro Statistics was written by and is associated to the ISBN: 9781943450039. This textbook survival guide was created for the textbook: OpenIntro Statistics, edition: 3.

Key Statistics Terms and definitions covered in this textbook
  • 2 k factorial experiment.

    A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

  • Bernoulli trials

    Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

  • Bias

    An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

  • Biased estimator

    Unbiased estimator.

  • Binomial random variable

    A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

  • Bivariate normal distribution

    The joint distribution of two normal random variables

  • Comparative experiment

    An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

  • Consistent estimator

    An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

  • Continuous uniform random variable

    A continuous random variable with range of a inite interval and a constant probability density function.

  • Correction factor

    A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

  • Covariance matrix

    A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

  • Critical region

    In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

  • Curvilinear regression

    An expression sometimes used for nonlinear regression models or polynomial regression models.

  • Eficiency

    A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

  • Erlang random variable

    A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

  • Error mean square

    The error sum of squares divided by its number of degrees of freedom.

  • Event

    A subset of a sample space.

  • Exponential random variable

    A series of tests in which changes are made to the system under study

  • F-test

    Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

  • Harmonic mean

    The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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