- 2.5.1E: If X and Y are independent random variables with means ?X = 9.5 and...
- 2.5.2E: The bottom of a cylindrical container has an area of 10 cm2. The co...
- 2.5.3E: The lifetime of a certain transistor in a certain application has m...
- 2.5.4E: Two batteries, with voltages V1 and V2, are connected in series. Th...
- 2.5.5E: A laminated item is composed of five layers. The layers are a simpl...
- 2.5.6E: Two independent measurements are made of the lifetime of a charmed ...
- 2.5.7E: The morality of a solute in solution is defined to be the number of...
- 2.5.8E: A machine that fills bottles with a beverage has a fill volume whos...
- 2.5.9E: The four sides of a picture frame consist of two pieces selected fr...
- 2.5.10E: A gas station earns $2.60 in revenue for each gallon of regular gas...
- 2.5.11E: A certain commercial jet plane uses a mean of 0.15 gallons of fuel ...
- 2.5.12E: The Needleman-Wunsch method for aligning DNA sequences assigns 1 po...
- 2.5.13E: In the article “An Investigation of the Ca–CO3–CaF2–K2SiO3–SiO2–Fe ...
- 2.5.14E: The oxygen equivalence number of a weld is a number that can be use...
- 2.5.15E: Measurements are made on the length and width (in cm) of a rectangu...
- 2.5.16E: The thickness Xof a wooden shim (in mm) has probability density fun...
- 2.5.17E: The article “Abyssal Peridotites > 3800 Ma from Southern West Green...
- 2.5.18E: The number of bytes downloaded per second on an information channel...
Solutions for Chapter 2.5: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 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.
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
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
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.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
The mean of the conditional probability distribution of a random variable.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
An expression sometimes used for nonlinear regression models or polynomial regression models.
A probability distribution for a discrete random variable
Another name for a cumulative distribution function.
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
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
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
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 .
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .