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# Solutions for Chapter 3-1: DISCRETE RANDOM VARIABLES

## Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition

ISBN: 9780471204541

Solutions for Chapter 3-1: DISCRETE RANDOM VARIABLES

Solutions for Chapter 3-1
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##### ISBN: 9780471204541

Chapter 3-1: DISCRETE RANDOM VARIABLES includes 12 full step-by-step solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 3. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780471204541. This expansive textbook survival guide covers the following chapters and their solutions. Since 12 problems in chapter 3-1: DISCRETE RANDOM VARIABLES have been answered, more than 19628 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

• Analytic study

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

• 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.

• 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.

• Central tendency

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.

• Chance cause

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

• Comparative experiment

An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

• Conditional probability density function

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

• Continuous random variable.

A random variable with an interval (either inite or ininite) of real numbers for its range.

• Control limits

See Control chart.

• Convolution

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.

• Cook’s distance

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• 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.

• Critical value(s)

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass function.

• Experiment

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

• Forward selection

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

• Geometric mean.

The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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