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Solutions for Chapter 3.10: Random Variables and Distributions

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

Full solutions for Probability and Statistics | 4th Edition

ISBN: 9780321500465

Probability and Statistics | 4th Edition | ISBN: 9780321500465 | Authors: Morris H. DeGroot, Mark J. Schervish

Solutions for Chapter 3.10: Random Variables and Distributions

Solutions for Chapter 3.10
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Textbook: Probability and Statistics
Edition: 4
Author: Morris H. DeGroot, Mark J. Schervish
ISBN: 9780321500465

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Probability and Statistics was written by and is associated to the ISBN: 9780321500465. Chapter 3.10: Random Variables and Distributions includes 20 full step-by-step solutions. Since 20 problems in chapter 3.10: Random Variables and Distributions have been answered, more than 16558 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
  • 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

  • Attribute

    A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

  • Bimodal distribution.

    A distribution with two modes

  • Binomial random variable

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

  • 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).

  • Coeficient of determination

    See R 2 .

  • Conditional mean

    The mean of the conditional probability distribution of a random variable.

  • Conditional probability mass function

    The probability mass function of the conditional probability distribution of a discrete random variable.

  • Contingency table.

    A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

  • Continuity correction.

    A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

  • 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.

  • Control chart

    A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

  • 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.

  • Decision interval

    A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

  • Dependent variable

    The response variable in regression or a designed experiment.

  • Distribution free method(s)

    Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

  • Empirical model

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

  • Event

    A subset of a sample space.

  • F distribution.

    The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

  • 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.

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