- 2.1.1E: The probability that a bearing fails during the first month of use ...
- 2.1.2E: A die (six faces) has the number 1 painted on three of its faces, t...
- 2.1.3E: A section of an exam contains four True-False questions. A complete...
- 2.1.4E: Three times each day, a quality engineer samples a component from a...
- 2.1.5E: Four candidates are to be interviewed for a job. Two of them, numbe...
- 2.1.6E: Refer to Exercise 5. Two candidates are randomly selected.a. List t...
- 2.1.7E: In a survey of households with television sets, the proportion of t...
- 2.1.8E: An automobile insurance company divides customers into three catego...
- 2.1.9E: Among the cast aluminum parts manufactured on a certain day, 80% we...
- 2.1.10E: The article “High Cumulative Risk of Lung Cancer Death among Smoker...
- 2.1.11E: A quality-control engineer samples 100 items manufactured by a cert...
- 2.1.12E: Let V be the event that a computer contains a virus, and let W be t...
- 2.1.13E: Let S be the event that a randomly selected college student has tak...
- 2.1.14E: Six hundred paving stones were examined for cracks, and 15 were fou...
- 2.1.15E: All the fourth -graders in a certain elementary school took a stand...
- 2.1.16E: A system contains two components, A and B. The system will function...
- 2.1.17E: A system contains two components, A and B. The system will function...
- 2.1.18E: Human blood may contain either or both of two antigens, A and B. Bl...
- 2.1.19E: True or false: If A and B are mutually exclusive,a. P (A?B) = 0____...
- 2.1.20E: A flywheel is attached to a crankshaft by 12 bolts, numbered 1 thro...
Solutions for Chapter 2.1: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th 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
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
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.
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
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.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
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.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Estimate (or point estimate)
The numerical value of a point estimator.
A property of a collection of events that indicates that their union equals the sample space.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
A signal from a control chart when no assignable causes are present
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
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.