Solutions for Chapter 2.9: Independent Random Vaariables

Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition | ISBN: 9781119285427 | Authors: Kishor S. Trivedi

Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition

ISBN: 9781119285427

Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition | ISBN: 9781119285427 | Authors: Kishor S. Trivedi

Solutions for Chapter 2.9: Independent Random Vaariables

Since 6 problems in chapter 2.9: Independent Random Vaariables have been answered, more than 1739 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by and is associated to the ISBN: 9781119285427. Chapter 2.9: Independent Random Vaariables includes 6 full step-by-step solutions.

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

    A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

  • 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.

  • Average run length, or ARL

    The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

  • Backward elimination

    A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

  • Binomial random variable

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

  • Bivariate distribution

    The joint probability distribution of two random variables.

  • Causal variable

    When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

  • Chi-square (or chi-squared) random variable

    A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

  • Cook’s distance

    In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

  • 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).

  • Covariance

    A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

  • 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.

  • Cumulative sum control chart (CUSUM)

    A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

  • Defect concentration diagram

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

  • Deming’s 14 points.

    A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

  • Error mean square

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

  • Error variance

    The variance of an error term or component in a model.

  • Experiment

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

  • Fraction defective

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

  • Gamma random variable

    A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

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