 4.4.17: You have two groups of distinctly differentitems, 10 in the first g...
 4.4.18: You have three groups of distinctly differentitems, four in the fir...
 4.4.19: Permutations Evaluate the following permutations.(HINT: Your scient...
 4.4.20: Combinations Evaluate these combinations:a. C53 b. C109 c. C66 d. C201
 4.4.21: Choosing People In how many ways can youselect five people from a g...
 4.4.22: Choosing People, again In how many wayscan you select two people fr...
 4.4.23: Dice Three dice are tossed. How many simpleevents are in the sample...
 4.4.24: Coins Four coins are tossed. How many simpleevents are in the sampl...
 4.4.25: The Urn Problem, again Three balls areselected from a box containin...
 4.4.26: What to Wear? You own 4 pairs of jeans, 12clean Tshirts, and 4 wea...
 4.4.27: 7 Itineraries A businessman in New York ispreparing an itinerary fo...
 4.4.28: Vacation Plans Your family vacation involvesa crosscountry air fli...
 4.4.29: A Card Game Three students are playing acard game. They decide to c...
 4.4.30: Dinner at Gerards A French restaurant inRiverside, California, offe...
 4.4.31: Playing Poker Five cards are selected from a52card deck for a poke...
 4.4.32: Poker II Refer to Exercise 4.31. You have apoker hand containing fo...
 4.4.33: A Hospital Survey A study is to be conductedin a hospital to determ...
 4.4.34: Traffic Two city council membersare to be selected from a total of ...
 4.4.35: The WNBA Professional basketball is now areality for women basketba...
 4.4.36: 6 100Meter Run, again Refer to Exercise 4.14,in which a 100meter ...
 4.4.37: Gender Bias? A woman brought a complaintof gender discrimination to...
 4.4.38: Cramming A student prepares for an examby studying a list of 10 pro...
 4.4.39: Monkey Business A monkey is given12 blocks: 3 shaped like squares, ...
Solutions for Chapter 4.4: Useful Counting Rules (Optional)
Full solutions for Introduction to Probability and Statistics 1  14th Edition
ISBN: 9781133103752
Solutions for Chapter 4.4: Useful Counting Rules (Optional)
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`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).

Acceptance region
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

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.

All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

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

Arithmetic mean
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

Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Chance cause
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.

Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.

Conidence interval
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

Defect
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.

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.

Deming
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Geometric mean.
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 .