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# Solutions for Chapter 3-2: PROBABILITY DISTRIBUTIONS AND PROBABILITY MASS FUNCTIONS

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

ISBN: 9780471204541

Solutions for Chapter 3-2: PROBABILITY DISTRIBUTIONS AND PROBABILITY MASS FUNCTIONS

Solutions for Chapter 3-2
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##### ISBN: 9780471204541

This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3-2: PROBABILITY DISTRIBUTIONS AND PROBABILITY MASS FUNCTIONS includes 13 full step-by-step solutions. Since 13 problems in chapter 3-2: PROBABILITY DISTRIBUTIONS AND PROBABILITY MASS FUNCTIONS have been answered, more than 19566 students have viewed full step-by-step solutions from this chapter. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780471204541.

Key Statistics Terms and definitions covered in this textbook
• `-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).

• 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

• 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.

• All possible (subsets) regressions

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• 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

• Bimodal distribution.

A distribution with two modes

• 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.

• Conditional variance.

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

• 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.

• 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).

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• Designed experiment

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

• Eficiency

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Event

A subset of a sample space.

• False alarm

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

• Finite population correction factor

A term in the formula for the variance of a hypergeometric random variable.

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

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