- 2-3.2-49: 2-49. If , and determine the following probabilities:
- 2-3.2-50: 2-50. If A, B, and C are mutually exclusive events with and determi...
- 2-3.2-51: 2-51. If A, B, and C are mutually exclusive events, is it possible ...
- 2-3.2-52: 2-52. Disks of polycarbonate plastic from a supplier are analyzed f...
- 2-3.2-53: 2-53. The analysis of shafts for a compressor is summarized by conf...
- 2-3.2-54: Cooking oil is produced in two main varieties: monoand polyunsatura...
- 2-3.2-55: 2-55. A manufacturer of front lights for automobiles tests lamps un...
- 2-3.2-56: The shafts in Exercise 2-53 are further classified in terms of the ...
Solutions for Chapter 2-3: ADDITION RULES
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
See Arithmetic mean.
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
The joint probability distribution of two random variables.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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.
A subset of effects in a fractional factorial design that deine the aliases in the design.
The response variable in regression or a designed experiment.
The amount of variability exhibited by data
Error of estimation
The difference between an estimated value and the true value.
A property of a collection of events that indicates that their union equals the sample space.
Exponential random variable
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
Fraction defective control chart
See P chart
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
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 .
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .