- 9.1: An urn contains 100 chips of which 20 are blue, 30 are red, and 50 ...
- 9.2: Let X be the smallest number obtained in rolling a balanced die n t...
- 9.3: Suppose that n points are selected at random and independently insi...
- 9.4: The joint probability density function of random variables X, Y , a...
- 9.5: A fair die is tossed 18 times. What is the probability that each fa...
- 9.6: Alvie, a marksman, fires seven independent shots at a target. Suppo...
- 9.7: A system consists of n components whose lifetimes form an independe...
- 9.8: A system consists of n components whose lifetimes form an independe...
- 9.9: A bar of length $ is broken into three pieces at two random spots. ...
- 9.10: Let X1, X2, and X3 be independent random variables from (0, 1). Fin...
Solutions for Chapter 9: Multivariate Distributions
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
Coeficient of determination
See R 2 .
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
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.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A matrix that provides the tests that are to be conducted in an 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).
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
Estimate (or point estimate)
The numerical value of a point estimator.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
Fraction defective control chart
See P chart
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.