- 4.2.1E: Let X ? Bin(7, 0.3). Finda. P(X = 1)________________b. P(X = 2)____...
- 4.2.2E: Let X ~ Bin(9, 0.4). Finda. P(X > 6)________________b. P(X ? 2)____...
- 4.2.3E: Find the following probabilities:a. P(X = 2) when X ? Bin(4, 0.6)__...
- 4.2.4E: At a certain airport, 75% of the flights arrive on time. A sample o...
- 4.2.5E: Of all the registered automobiles in a certain state, 10% violate t...
- 4.2.6E: A fair die is rolled 8 times.a. What is the probability that the di...
- 4.2.7E: Of all the weld failures in a certain assembly, 85% of them occur i...
- 4.2.8E: A general contracting firm experiences cost overruns on 20% of its ...
- 4.2.9E: Several million lottery tickets are sold, and 60% of the Tickets ar...
- 4.2.10E: A quality engineer takes a random sample of 100 steel rods from a d...
- 4.2.11E: In a random sample of 100 parts ordered from vendor A, 12 were defe...
- 4.2.12E: Of the items manufactured by a certain process, 20% are defective. ...
- 4.2.13E: Of the bolts manufactured for a certain application, 90% meet the l...
- 4.2.14E: Gears produced by a grinding process are categorized either as conf...
- 4.2.15E: A commuter must pass through three traffic lights on her way to wor...
- 4.2.16E: A distributor receives a large shipment of components. The distribu...
- 4.2.17E: A k out of n system is one in which there is a group of n component...
- 4.2.18E: Refer to Exercise 17 for the definition of a k out of n system. For...
- 4.2.19E: A certain large shipment comes with a guarantee that it contains no...
- 4.2.20E: An insurance company offers a discount to homeowners who install sm...
- 4.2.21E: A message consists of a string of bits (0s and1s). Due to noise in ...
- 4.2.22E: Let X ~ Bin(n, p), and let Y = n ? X. Show that Y ~ Bin(n, 1 ? p).
- 4.2.23E: Porcelain figurines are sold for $10 if flawless, and for $3 if the...
- 4.2.24E: One design for a system requires the installation of two identical ...
- 4.2.25E: Refer to Example 4.14. Estimate the probability that exactly one of...
- 4.2.26E: If p is a success probability, the quantity p/( 1 ? p) is called th...
Solutions for Chapter 4.2: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
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.
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
See Arithmetic mean.
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.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
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.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
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
Another term for the conidence coeficient.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
The amount of variability exhibited by data
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 variance of an error term or component in a model.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
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 .