- 2.1.1: Four universities1, 2, 3, and 4are participating in aholiday basket...
- 2.1.10: a. In Example 2.10, identify three events that are mutuallyexclusiv...
- 2.1.2: Suppose that vehicles taking a particular freeway exitcan turn righ...
- 2.1.3: Three components are connected to form a system asshown in the acco...
- 2.1.4: Each of a sample of four home mortgages is classified asfixed rate ...
- 2.1.5: A family consisting of three personsA, B, and Cgoesto a medical cli...
- 2.1.6: A college library has five copies of a certain text onreserve. Two ...
- 2.1.7: An academic department has just completed voting bysecret ballot fo...
- 2.1.8: An engineering construction firm is currently workingon power plant...
- 2.1.9: Use Venn diagrams to verify the following two relationshipsfor any ...
Solutions for Chapter 2.1: Sample Spaces and Events
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
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.
See Arithmetic mean.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Box plot (or box and whisker plot)
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 mean of the conditional probability distribution of a random variable.
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.
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
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r