 3.8.1: Given n random numbers u1, u2,...,un, derive an expression for a ra...
 3.8.2: Compare the TMR/simplex reliability with twocomponent and threeco...
 3.8.3: Repeat problem 2 for two and three component parallel redundant sys...
 3.8.4: Show that the reliability expression (3.78) for koutofn system r...
 3.8.5: Using equation (3.80) obtain an explicit expression for the reliabi...
Solutions for Chapter 3.8: Distribution Of Sums
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications  2nd Edition
ISBN: 9781119285427
Solutions for Chapter 3.8: Distribution Of Sums
Get Full SolutionsThis textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Since 5 problems in chapter 3.8: Distribution Of Sums have been answered, more than 1087 students have viewed full stepbystep solutions from this chapter. Chapter 3.8: Distribution Of Sums includes 5 full stepbystep solutions. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by Patricia and is associated to the ISBN: 9781119285427.

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

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Attribute
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

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

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

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.

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 probability
The probability of an event given that the random experiment produces an outcome in another event.

Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.

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

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Dependent variable
The response variable in regression or a designed experiment.

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

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

Error variance
The variance of an error term or component in a model.

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

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

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.

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .
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