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Solutions for Chapter 5.2: Distributions of Functions of Random Variables

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Full solutions for Probability and Statistical Inference | 9th Edition

ISBN: 9780321923271

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Solutions for Chapter 5.2: Distributions of Functions of Random Variables

Solutions for Chapter 5.2
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Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.2: Distributions of Functions of Random Variables includes 31 full step-by-step solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Since 31 problems in chapter 5.2: Distributions of Functions of Random Variables have been answered, more than 58492 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
  • Additivity property of x 2

    If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

  • All possible (subsets) regressions

    A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

  • Bias

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

  • Binomial random variable

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

  • Coeficient of determination

    See R 2 .

  • Combination.

    A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

  • Conditional probability

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

  • Conditional variance.

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

  • Confounding

    When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

  • Conidence coeficient

    The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

  • Consistent estimator

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

  • Contingency table.

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

  • Continuous random variable.

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

  • 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.

  • Deming

    W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

  • Erlang random variable

    A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

  • 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.

  • Gamma function

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

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