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# Solutions for Chapter 12.4: Simulation

## Full solutions for Probability and Statistics | 4th Edition

ISBN: 9780321500465

Solutions for Chapter 12.4: Simulation

Solutions for Chapter 12.4
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##### ISBN: 9780321500465

Probability and Statistics was written by and is associated to the ISBN: 9780321500465. This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Chapter 12.4: Simulation includes 17 full step-by-step solutions. Since 17 problems in chapter 12.4: Simulation have been answered, more than 15750 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Bayes’ estimator

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

• Bayes’ theorem

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

• Bias

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

• Causal variable

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

• 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.

• Combination.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

• Conditional probability mass function

The probability mass function of the conditional probability distribution of a discrete 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

• Continuity correction.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

• 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.

• 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.

• Deming’s 14 points.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

• Dispersion

The amount of variability exhibited by data

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Event

A subset of a sample space.

• 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.

• Exponential random variable

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

• 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.

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