- 9.3.1: Light bulbs manufactured by a certain factory last a random time be...
- 9.3.2: An urn contains 100 chips of which 20 are blue, 30 are red, and 50 ...
- 9.3.3: Suppose that each day the price of a stock moves up 1/8 of a point ...
- 9.3.4: At a certain college, 16% of the calculus students get As, 34% Bs, ...
- 9.3.5: Suppose that 50% of the watermelons grown on a farm are classified ...
- 9.3.6: Suppose that the ages of 30% of the teachers of a country are over ...
- 9.3.7: (Genetics) As we know, in humans, for blood type, there are three a...
- 9.3.8: (Genetics) Let p and q be positive numbers with p + q = 1. For a ge...
- 9.3.9: Customers enter a department store at the rate of three per minute,...
Solutions for Chapter 9.3: Order Statistics
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
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
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.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
The joint probability distribution of two random variables.
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
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
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
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.
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
A probability distribution for a discrete random variable
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
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.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .