- 10.7.1: Suppose that a sample comprises the 15 observed values in Table 10....
- 10.7.2: Suppose that a sample comprises the 14 observed values in Table 10....
- 10.7.3: Suppose that a random sample of n = 100 observations is taken from ...
- 10.7.4: Suppose that a random sample of n = 100 observations is taken from ...
- 10.7.5: Let f (x) denote the p.d.f. of the contaminated normal distribution...
- 10.7.6: Use the data in Table 10.6 on page 640. We want an estimate of the ...
- 10.7.7: Suppose that X1,...,Xn are i.i.d. with a distribution that has the ...
- 10.7.8: If Fig. 10.8 were extended all the way to = 1, the variance of the ...
- 10.7.9: Assume that X1,...,Xn form a random sample from the distribution wi...
- 10.7.10: Let X1,...,Xn be i.i.d. with the p.d.f. in Eq. (10.7.5). Assume tha...
- 10.7.11: Let X be a random variable with a continuous distribution such that...
- 10.7.12: Let X be a random variable with a continuous distribution such that...
- 10.7.13: Find the median absolute deviation of the Cauchy distribution.
- 10.7.14: Let X have the exponential distribution with parameter . Prove that...
- 10.7.15: Let X have a normal distribution with standard deviation . a. Prove...
- 10.7.16: Darwin (1876, p. 16) reported the results of an experiment in which...
- 10.7.17: Let X1,...,Xn be a large random sample from a distribution with p.d...
Solutions for Chapter 10.7: Categorical Data and Nonparametric Methods
Full solutions for Probability and Statistics | 4th Edition
2 k factorial experiment.
A full factorial experiment with k factors and 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.
The joint probability distribution of two random variables.
Bivariate normal distribution
The joint distribution of two normal random variables
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
Formulas used to determine the number of elements in sample spaces and events.
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.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
A probability distribution for a discrete random variable
Discrete random variable
A random variable with a inite (or countably ininite) range.
A subset of a sample space.
A series of tests in which changes are made to the system under study
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.