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Get Full Access to Statistics - Textbook Survival Guide
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# Solutions for Chapter 1.5: Relative Frequency Histograms

## Full solutions for Introduction to Probability and Statistics 1 | 14th Edition

ISBN: 9781133103752

Solutions for Chapter 1.5: Relative Frequency Histograms

Solutions for Chapter 1.5
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##### ISBN: 9781133103752

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.5: Relative Frequency Histograms includes 52 full step-by-step solutions. Since 52 problems in chapter 1.5: Relative Frequency Histograms have been answered, more than 10505 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 1, edition: 14. Introduction to Probability and Statistics 1 was written by and is associated to the ISBN: 9781133103752.

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).

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).

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• Central composite design (CCD)

A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.

• 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.

• Combination.

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

• Continuous uniform random variable

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

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• 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 .

• 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 .

• Covariance matrix

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• Critical value(s)

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

• Curvilinear regression

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

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• Discrete distribution

A probability distribution for a discrete random variable

• 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.

• Event

A subset of a sample space.

• Gamma random variable

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

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

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