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# Solutions for Chapter 1.1: Definitions and Terminology

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

ISBN: 9781449691721

Solutions for Chapter 1.1: Definitions and Terminology

Solutions for Chapter 1.1
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##### ISBN: 9781449691721

Since 60 problems in chapter 1.1: Definitions and Terminology have been answered, more than 35033 students have viewed full step-by-step solutions from this chapter. 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. Chapter 1.1: Definitions and Terminology includes 60 full step-by-step solutions. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721.

Key Statistics Terms and definitions covered in this textbook
• 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.

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Bimodal distribution.

A distribution with two modes

• C chart

An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

• Causal variable

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

• Conditional probability density function

The probability density function of the conditional probability distribution of a continuous random variable.

• Conidence interval

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

• Conidence level

Another term for the conidence coeficient.

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Cumulative distribution function

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

• Defects-per-unit control chart

See U chart

• Dispersion

The amount of variability exhibited by data

• Distribution function

Another name for a cumulative distribution function.

• 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.

• Expected value

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.

• False alarm

A signal from a control chart when no assignable causes are present

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

• Fraction defective control chart

See P chart

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