- 1.6.1: If two balanced dice are rolled, what is the probability that the s...
- 1.6.2: If two balanced dice are rolled, what is the probability that the s...
- 1.6.3: If two balanced dice are rolled, what is the probability that the d...
- 1.6.4: A school contains students in grades 1, 2, 3, 4, 5, and 6. Grades 2...
- 1.6.5: For the conditions of Exercise 4, what is the probability that the ...
- 1.6.6: If three fair coins are tossed, what is the probability that all th...
- 1.6.7: Consider the setup of Example 1.6.4 on page 23. This time, assume t...
- 1.6.8: Consider an experiment in which a fair coin is tossed once and a ba...
Solutions for Chapter 1.6: Introduction to Probability
Full solutions for Probability and Statistics | 4th Edition
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).
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
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
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.
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.
The mean of the conditional probability distribution of a random variable.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A probability distribution for a continuous random variable.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
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.
A signal from a control chart when no assignable causes are present
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
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .