Solutions for Chapter 4: Random Variables and Expectation

Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition | ISBN: 9780123948113 | Authors: Sheldon M. Ross

Full solutions for Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition

ISBN: 9780123948113

Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition | ISBN: 9780123948113 | Authors: Sheldon M. Ross

Solutions for Chapter 4: Random Variables and Expectation

Solutions for Chapter 4
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Textbook: Introduction to Probability and Statistics for Engineers and Scientists
Edition: 5
Author: Sheldon M. Ross
ISBN: 9780123948113

Since 57 problems in chapter 4: Random Variables and Expectation have been answered, more than 3676 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics for Engineers and Scientists, edition: 5. Chapter 4: Random Variables and Expectation includes 57 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Introduction to Probability and Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9780123948113.

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).

  • Acceptance region

    In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

  • Analytic study

    A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

  • Arithmetic mean

    The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

  • Attribute control chart

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

  • Bias

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

  • Bimodal distribution.

    A distribution with two modes

  • Bivariate distribution

    The joint probability distribution of two random variables.

  • Central tendency

    The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

  • 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

  • Control limits

    See Control chart.

  • Correction factor

    A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

  • 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

  • Curvilinear regression

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

  • Discrete random variable

    A random variable with a inite (or countably ininite) range.

  • Distribution function

    Another name for a cumulative distribution function.

  • Error of estimation

    The difference between an estimated value and the true value.

  • Expected value

    The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

  • Exponential random variable

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

  • F-test

    Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

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