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# Solutions for Chapter 4.4: Additional Operational Properties

## Full solutions for Advanced Engineering Mathematics | 5th Edition

ISBN: 9781449691721

Solutions for Chapter 4.4: Additional Operational Properties

Solutions for Chapter 4.4
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##### ISBN: 9781449691721

Chapter 4.4: Additional Operational Properties includes 68 full step-by-step solutions. Since 68 problems in chapter 4.4: Additional Operational Properties have been answered, more than 34882 students have viewed full step-by-step solutions from this chapter. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• 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

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Causal variable

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

• 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.

• Coeficient of determination

See R 2 .

• 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.

• Conditional mean

The mean of the conditional probability distribution of a random variable.

• Contingency table.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

• Control chart

A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

• Control limits

See Control chart.

• Critical region

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• Erlang random variable

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

• Event

A subset of a sample space.

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• Experiment

A series of tests in which changes are made to the system under study

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

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