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Solutions for Chapter 1: Introduction

Mathematical Statistics with Applications | 8th Edition | ISBN: 9780321807090 | Authors: Irwin Miller

Full solutions for Mathematical Statistics with Applications | 8th Edition

ISBN: 9780321807090

Mathematical Statistics with Applications | 8th Edition | ISBN: 9780321807090 | Authors: Irwin Miller

Solutions for Chapter 1: Introduction

Solutions for Chapter 1
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Chapter 1: Introduction includes 1 full step-by-step solutions. Since 1 problems in chapter 1: Introduction have been answered, more than 280 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications, edition: 8. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780321807090. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
  • Addition rule

    A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

  • Additivity property of x 2

    If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

  • Axioms of probability

    A set of rules that probabilities deined on a sample space must follow. See Probability

  • Bias

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

  • Biased estimator

    Unbiased estimator.

  • Block

    In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

  • 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 composite design (CCD)

    A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.

  • Conditional probability density function

    The probability density function of the conditional probability distribution of a continuous random variable.

  • Consistent estimator

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

  • Continuous distribution

    A probability distribution for a continuous random variable.

  • Correlation

    In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

  • Counting techniques

    Formulas used to determine the number of elements in sample spaces and events.

  • 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.

  • Curvilinear regression

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

  • 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).

  • Estimate (or point estimate)

    The numerical value of a point estimator.

  • Exponential random variable

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

  • Fractional factorial experiment

    A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

  • Generator

    Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

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