- 7.8.1: . A gamma distribution for which both parameters and are unknown ( ...
- 7.8.2: A beta distribution for which both parameters and are unknown ( > 0...
- 7.8.3: A Pareto distribution (see Exercise 16 of Sec. 5.7) for which both ...
- 7.8.4: The uniform distribution on the interval [, + 3], where the value o...
- 7.8.5: Suppose that the vectors (X1, Y1), (X2, Y2), . . . , (Xn, Yn) form ...
- 7.8.6: Consider a distribution for which the p.d.f. or the p.f. is f (x| )...
- 7.8.7: Show that each of the following families of distributions is a two-...
- 7.8.8: Suppose that X1,...,Xn form a random sample from an exponential dis...
- 7.8.9: Suppose that X1,...,Xn form a random sample from the Bernoulli dist...
- 7.8.10: Suppose that X1,...,Xn form a random sample from the uniform distri...
- 7.8.11: Suppose that X1,...,Xn form a random sample from a Cauchy distribut...
- 7.8.12: Suppose that X1,...,Xn form a random sample from a distribution for...
- 7.8.13: Suppose that X1,...,Xn form a random sample from the uniform distri...
- 7.8.14: For the conditions of Exercise 5, the M.L.E.s of the means, the var...
- 7.8.15: Suppose that X1,...,Xn form a random sample from the Bernoulli dist...
- 7.8.16: Suppose that X1,...,Xn form a random sample from a Poisson distribu...
- 7.8.17: Suppose that X1,...,Xn form a random sample from a normal distribut...
Solutions for Chapter 7.8: Estimation
Full solutions for Probability and Statistics | 4th Edition
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
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
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 distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
A probability distribution for a continuous random variable.
See Control chart.
The response variable in regression or a designed experiment.
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Estimate (or point estimate)
The numerical value of a point estimator.
A series of tests in which changes are made to the system under study
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
A function used in the probability density function of a gamma random variable that can be considered to extend factorials