- 3-5.3-46: Let the random variable X have a discrete uniform distribution on t...
- 3-5.3-47: 3-47. Let the random variable X have a discrete uniform distributio...
- 3-5.3-48: Let the random variable X be equally likely to assume any of the va...
- 3-5.3-49: 3-49. Thickness measurements of a coating process are made to the n...
- 3-5.3-50: Product codes of 2, 3, or 4 letters are equally likely. What is the...
- 3-5.3-51: 3-51. The lengths of plate glass parts are measured to the nearest ...
- 3-5.3-52: Suppose that X has a discrete uniform distribution on the integers ...
- 3-5.3-53: Show that for a discrete uniform random variable X, if each of the ...
- 3-5.3-54: The probability of an operator entering alphanumeric data incorrect...
Solutions for Chapter 3-5: DISCRETE UNIFORM DISTRIBUTION
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
Coeficient of determination
See R 2 .
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.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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 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 distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
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.
Defects-per-unit control chart
See U chart
The response variable in regression or a designed experiment.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Error of estimation
The difference between an estimated value and the true value.
Exponential random variable
A series of tests in which changes are made to the system under study
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
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