 1.1.1: Two towns are connected by a network of communication channels. The...
 1.1.2: Given three components with respective reliabilities R1 = 0.8, R2 =...
 1.1.3: Determine the conditions under which an event A is independent of i...
 1.1.4: General multiplication rule (GMR). Given a list of events A1, A2, ,...
 1.1.5: Seven lamps are located as shown in Figure 1.P.3. Each lamp can fai...
 1.1.6: Consider a base repeater in a cellular communication system with tw...
 1.1.7: Modify the base repeater problem above so that a control can also f...
 1.1.8: Return to Example 1.13 but now permitting a shared link BC as shown...
Solutions for Chapter 1.1: Independence of Events
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications  2nd Edition
ISBN: 9781119285427
Solutions for Chapter 1.1: Independence of Events
Get Full SolutionsProbability and Statistics with Reliability, Queuing, and Computer Science Applications was written by Patricia and is associated to the ISBN: 9781119285427. Chapter 1.1: Independence of Events includes 8 full stepbystep solutions. Since 8 problems in chapter 1.1: Independence of Events have been answered, more than 1271 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2.

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.

Biased estimator
Unbiased estimator.

Conditional variance.
The variance of the conditional probability distribution of a 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

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

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol 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 incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Control limits
See Control chart.

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.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

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.

Deming
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

Discrete distribution
A probability distribution for a discrete random variable

Dispersion
The amount of variability exhibited by data

Distribution function
Another name for a cumulative distribution function.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

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

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

Generator
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

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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