- 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
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.
The variance of the conditional probability distribution of a random variable.
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
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
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.
See Control chart.
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.
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 .
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 .
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A probability distribution for a discrete random variable
The amount of variability exhibited by data
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.
A signal from a control chart when no assignable causes are present
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
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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