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Solutions for Chapter 3.9: 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 3.9: Random Variables and Distributions

Solutions for Chapter 3.9
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Textbook: Probability and Statistics
Edition: 4
Author: Morris H. DeGroot, Mark J. Schervish
ISBN: 9780321500465

Probability and Statistics was written by and is associated to the ISBN: 9780321500465. Since 21 problems in chapter 3.9: Random Variables and Distributions have been answered, more than 15828 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, edition: 4. Chapter 3.9: Random Variables and Distributions includes 21 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
  • 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

  • Addition rule

    A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

  • Analysis of variance (ANOVA)

    A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

  • Assignable cause

    The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

  • 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.

  • Bayes’ theorem

    An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

  • Bivariate normal distribution

    The joint distribution of two normal random variables

  • 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).

  • Chance cause

    The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

  • Conditional mean

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

  • Conditional probability distribution

    The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

  • Continuous distribution

    A probability distribution for a continuous 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 .

  • Cumulative normal distribution function

    The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

  • Dependent variable

    The response variable in regression or a designed experiment.

  • Exhaustive

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

  • 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.

  • Finite population correction factor

    A term in the formula for the variance of a hypergeometric random variable.

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