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Solutions for Chapter 6.1: Introduction

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 6.1: Introduction

Solutions for Chapter 6.1
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Chapter 6.1: Introduction includes 2 full step-by-step solutions. This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by and is associated to the ISBN: 9781119285427. Since 2 problems in chapter 6.1: Introduction have been answered, more than 3396 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
  • Average

    See Arithmetic mean.

  • 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).

  • Center line

    A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

  • Consistent estimator

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

  • Continuous random variable.

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

  • 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).

  • Critical value(s)

    The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

  • Density function

    Another name for a probability density function

  • 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.

  • Estimator (or point estimator)

    A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

  • Exhaustive

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

  • Exponential random variable

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

  • Fisher’s least signiicant difference (LSD) method

    A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

  • 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.

  • Frequency distribution

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

  • Gamma function

    A function used in the probability density function of a gamma random variable that can be considered to extend factorials

  • Gamma random variable

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

  • Goodness of fit

    In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

  • Hat matrix.

    In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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