- 4.4.35E: Suppose that f (x) = 0.25 for 0 < x < 4. Determine the mean and var...
- 4.4.36E: Suppose that f (x) = 0.125x for 0 < x < 4. Determine the mean and v...
- 4.4.37E: Suppose that f (x) = 1.5x2 for ?1< x < 1. Determine the mean and va...
- 4.4.38E: Suppose that f (x) = x / 8 for 3 < x < 5. Determine the mean and va...
- 4.4.39E: ?Determine the mean and variance of the random variable in Exercise...
- 4.4.40E: ?Determine the mean and variance of the random variable in Exercise...
- 4.4.41E: ?Determine the mean and variance of the random variable in Exercise...
- 4.4.42E: ?Determine the mean and variance of the random variable in Exercise...
- 4.4.43E: ?Determine the mean and variance of the random variable in Exercise...
- 4.4.44E: ?Determine the mean and variance of the random variable in Exercise...
- 4.4.45E: Suppose that contamination particle size (in micrometers) can be mo...
- 4.4.46E: Suppose that the probability density function of the length of comp...
- 4.4.47E: The thickness of a conductive coating in micrometers has a density ...
- 4.4.48E: The probability density function of the weight of packages delivere...
- 4.4.49E: Integration by parts is required. The probability density function ...
Solutions for Chapter 4.4: Applied Statistics and Probability for Engineers 6th Edition
Full solutions for Applied Statistics and Probability for Engineers | 6th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
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).
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
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.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
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.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
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.
Defects-per-unit control chart
See U chart
A subset of effects in a fractional factorial design that deine the aliases in the design.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A matrix that provides the tests that are to be conducted in an experiment.
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.