- 2-4.2-57: 2-57. Disks of polycarbonate plastic from a supplier are analyzed f...
- 2-4.2-58: Samples of a cast aluminum part are classified on the basis of surf...
- 2-4.2-59: 2-59. The analysis of shafts for a compressor is summarized by conf...
- 2-4.2-60: The following table summarizes the analysis of samples of galvanize...
- 2-4.2-61: 2-61. Consider the data on wafer contamination and location in the ...
- 2-4.2-62: A lot of 100 semiconductor chips contains 20 that are defective. Tw...
- 2-4.2-63: 2-63. A lot contains 15 castings from a local supplier and 25 casti...
- 2-4.2-64: Continuation of Exercise 2-63. Suppose three castings are selected ...
- 2-4.2-65: 2-65. A batch of 500 containers for frozen orange juice contains 5 ...
- 2-4.2-66: Continuation of Exercise 2-65. Three containers are selected, at ra...
- 2-4.2-67: 2-67. A maintenance firm has gathered the following information reg...
- 2-4.2-68: If , must A B? Draw a Venn diagram to explain your answer
- 2-4.2-69: Suppose A and B are mutually exclusive events. Construct a Venn dia...
Solutions for Chapter 2-4: CONDITIONAL PROBABILITY
Full solutions for Applied Statistics and Probability for Engineers | 3rd 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.
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
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
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.
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
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.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
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).
Estimate (or point estimate)
The numerical value of a point estimator.
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
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.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
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 .