Mathematical Statistics with Applications 7th Edition - Solutions by Chapter

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).

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

A distribution with two modes

The joint probability distribution of two random variables.

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).

The probability of an event given that the random experiment produces an outcome in another event.

The variance of the conditional probability distribution of a 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 .

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

A quality tool that graphically shows the location of defects on a part or in a process.

See U chart

The amount of variability exhibited by data

The error sum of squares divided by its number of degrees of freedom.

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

A term in the formula for the variance of a hypergeometric random variable.

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 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.