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Solutions for Chapter 4.5: Expectation

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

Full solutions for Probability and Statistics | 4th Edition

ISBN: 9780321500465

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

Solutions for Chapter 4.5: Expectation

Solutions for Chapter 4.5
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Textbook: Probability and Statistics
Edition: 4
Author: Morris H. DeGroot, Mark J. Schervish
ISBN: 9780321500465

This expansive textbook survival guide covers the following chapters and their solutions. Since 18 problems in chapter 4.5: Expectation have been answered, more than 15829 students have viewed full step-by-step solutions from this chapter. Probability and Statistics was written by and is associated to the ISBN: 9780321500465. Chapter 4.5: Expectation includes 18 full step-by-step solutions. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4.

Key Statistics Terms and definitions covered in this textbook
  • Acceptance region

    In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

  • C chart

    An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

  • Central limit theorem

    The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

  • Continuous random variable.

    A random variable with an interval (either inite or ininite) of real numbers for its range.

  • 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.

  • Crossed factors

    Another name for factors that are arranged in a factorial experiment.

  • Defect concentration diagram

    A quality tool that graphically shows the location of defects on a part or in a process.

  • Distribution free method(s)

    Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

  • Error mean square

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

  • Error propagation

    An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

  • Exhaustive

    A property of a collection of events that indicates that their union equals the sample space.

  • Expected value

    The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

  • Experiment

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

  • Extra sum of squares method

    A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

  • Forward selection

    A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

  • Fraction defective

    In statistical quality control, that portion of a number of units or the output of a process that is defective.

  • Frequency distribution

    An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

  • Generating function

    A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

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