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Solutions for Chapter 7: Functions of Random Variables

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 7: Functions of Random Variables

Solutions for Chapter 7
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Since 1 problems in chapter 7: Functions of Random Variables have been answered, more than 312 students have viewed full step-by-step solutions from this chapter. Chapter 7: Functions of Random Variables includes 1 full step-by-step solutions. 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
  • Bayes’ theorem

    An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

  • Box plot (or box and whisker plot)

    A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

  • Chi-square test

    Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

  • Conditional probability distribution

    The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

  • Conidence interval

    If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

  • Continuous distribution

    A probability distribution for a continuous random variable.

  • Contrast

    A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

  • Correlation coeficient

    A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

  • 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.

  • Defects-per-unit control chart

    See U chart

  • Deining relation

    A subset of effects in a fractional factorial design that deine the aliases in the design.

  • 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.

  • Empirical model

    A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

  • Erlang random variable

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

  • Error of estimation

    The difference between an estimated value and the true value.

  • 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.

  • 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.

  • Finite population correction factor

    A term in the formula for the variance of a hypergeometric random variable.

  • 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.

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