Solutions for Chapter 5.1: 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 5.1: Introduction

This expansive textbook survival guide covers the following chapters and their solutions. Since 5 problems in chapter 5.1: Introduction have been answered, more than 1277 students have viewed full step-by-step solutions from this chapter. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by Patricia and is associated to the ISBN: 9781119285427. Chapter 5.1: Introduction includes 5 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.

Key Statistics Terms and definitions covered in this textbook
  • a-error (or a-risk)

    In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

  • Alternative hypothesis

    In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

  • Attribute control chart

    Any control chart for a discrete random variable. See Variables control chart.

  • 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.

  • 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

    The probability of an event given that the random experiment produces an outcome in another event.

  • Continuous uniform random variable

    A continuous random variable with range of a inite interval and a constant probability density function.

  • Convolution

    A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

  • 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.

  • Degrees of freedom.

    The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

  • Empirical model

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

  • 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.

  • 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.

  • 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.

  • Gamma function

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

  • Generating function

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

  • 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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