- Chapter 1: Introduction to Statistics
- Chapter 10: Analysis of Variance
- Chapter 11: Goodness of Fit Tests and Categorical Data Analysis
- Chapter 12: Nonparametric Hypothesis Tests
- Chapter 13: Quality Control
- Chapter 14: Life Testing
- Chapter 15: Simulation, Bootstrap Statistical Methods, and Permutation Tests
- Chapter 2: Descriptive Statistics
- Chapter 3: Elements of Probability
- Chapter 4: Random Variables and Expectation
- Chapter 5: Special Random Variables
- Chapter 6: Distributions of Sampling Statistics
- Chapter 7: Parameter Estimation
- Chapter 8: Hypothesis Testing
- Chapter 9: Regression
Introduction to Probability and Statistics for Engineers and Scientists 5th Edition - Solutions by Chapter
Full solutions for Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition
Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition - Solutions by ChapterGet Full Solutions
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).
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
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.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
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.
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.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
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.
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 .
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Another name for a cumulative distribution function.
A subset of a sample space.
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.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.