- Chapter 10: Statistical Inference for Two Samples
- Chapter 11: Simple Linear Regression and Correlation
- Chapter 12: Multiple Linear Regression
- Chapter 13: Design and Analysis of Single-Factor Experiments: The Analysis of Variance
- Chapter 14: Design of Experiments with Several Factors
- Chapter 15: Statistical Quality Control
- Chapter 2: Probability
- Chapter 3: Discrete Random Variables and Probability Distributions
- Chapter 4: Continuous Random Variables and Probability Distributions
- Chapter 5: Joint Probability Distributions
- Chapter 6: Descriptive Statistics
- Chapter 7: Sampling Distributions and Point Estimation of Parameters
- Chapter 8: Statistical Intervals for a Single Sample
- Chapter 9: Tests of Hypotheses for a Single Sample
Applied Statistics and Probability for Engineers 5th Edition - Solutions by Chapter
Full solutions for Applied Statistics and Probability for Engineers | 5th Edition
Applied Statistics and Probability for Engineers | 5th Edition - Solutions by ChapterGet Full Solutions
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.
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
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
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 chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
The mean of the conditional probability distribution of a random variable.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
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
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
See Control chart.
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.
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 .
Discrete random variable
A random variable with a inite (or countably ininite) range.
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Estimate (or point estimate)
The numerical value of a point estimator.
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.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
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