- 7.2.1: Consider again the situation described in Example 7.2.8. This time,...
- 7.2.2: Suppose that the proportion of defective items in a large manufactu...
- 7.2.3: Suppose that the number of defects on a roll of magnetic recording ...
- 7.2.4: Suppose that the prior distribution of some parameter is a gamma di...
- 7.2.5: Suppose that the prior distribution of some parameter is a beta dis...
- 7.2.6: Suppose that the proportion of defective items in a large manufactu...
- 7.2.7: Consider again the problem described in Exercise 6, but suppose now...
- 7.2.8: Suppose that X1,...,Xn form a random sample from a distribution for...
- 7.2.9: Consider again the problem described in Exercise 6, and assume the ...
- 7.2.10: Suppose that a single observation X is to be taken from the uniform...
- 7.2.11: Consider again the conditions of Exercise 10, and assume the same p...
Solutions for Chapter 7.2: Estimation
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.
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.
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
See Arithmetic mean.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
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.
The probability of an event given that the random experiment produces an outcome in another event.
A probability distribution for a continuous random variable.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
Formulas used to determine the number of elements in sample spaces and events.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
Another name for a cumulative distribution function.
Error of estimation
The difference between an estimated value and the true value.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
A function used in the probability density function of a gamma random variable that can be considered to extend factorials