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Solutions for Chapter 5: Continuous Random Variables

First Course in Probability | 8th Edition | ISBN: 9780136033134 | Authors: Norman S. Nise

Full solutions for First Course in Probability | 8th Edition

ISBN: 9780136033134

First Course in Probability | 8th Edition | ISBN: 9780136033134 | Authors: Norman S. Nise

Solutions for Chapter 5: Continuous Random Variables

Solutions for Chapter 5
4 5 0 300 Reviews
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Textbook: First Course in Probability
Edition: 8
Author: Norman S. Nise
ISBN: 9780136033134

Summary of Chapter 5: Continuous Random Variables

Since 41 problems in chapter 5: Continuous Random Variables have been answered, more than 26609 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: First Course in Probability, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. First Course in Probability was written by and is associated to the ISBN: 9780136033134. Chapter 5: Continuous Random Variables includes 41 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
  • 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

  • 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

  • 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

  • Bias

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

  • Cause-and-effect diagram

    A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

  • Central limit theorem

    The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

  • Completely randomized design (or experiment)

    A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

  • 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

  • Continuous uniform random variable

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

  • 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.

  • 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 .

  • Defect

    Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

  • 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.

  • Discrete random variable

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

  • Eficiency

    A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

  • Extra sum of squares method

    A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

  • Fraction defective

    In statistical quality control, that portion of a number of units or the output of a process that is defective.

  • Gamma random variable

    A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

  • 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 .