 1.1: (a) How many different 7place license plates arepossible if the fi...
 1.2: How many outcome sequences are possible when adie is rolled four ti...
 1.3: Twenty workers are to be assigned to 20 differentjobs, one to each ...
 1.4: John, Jim, Jay, and Jack have formed a band consistingof 4 instrume...
 1.5: For years, telephone area codes in the UnitedStates and Canada cons...
 1.6: A wellknown nursery rhyme starts as follows:As I was going to St. ...
 1.7: (a) In how many ways can 3 boys and 3 girls sit ina row?(b) In how ...
 1.8: How many different letter arrangements can bemade from the letters(...
 1.9: A child has 12 blocks, of which 6 are black, 4 arered, 1 is white, ...
 1.10: In how many ways can 8 people be seated in arow if(a) there are no ...
 1.11: In how many ways can 3 novels, 2 mathematicsbooks, and 1 chemistry ...
 1.12: Five separate awards (best scholarship, best leadershipqualities, a...
 1.13: Consider a group of 20 people. If everyone shakeshands with everyon...
 1.14: How many 5card poker hands are there?
 1.15: A dance class consists of 22 students, of which 10are women and 12 ...
 1.16: A student has to sell 2 books from a collection of6 math, 7 science...
 1.17: Seven different gifts are to be distributed among10 children. How m...
 1.18: A committee of 7, consisting of 2 Republicans,2 Democrats, and 3 In...
 1.19: From a group of 8 women and 6 men, a committeeconsisting of 3 men a...
 1.20: A person has 8 friends, of whom 5 will be invitedto a party.(a) How...
 1.21: Consider the grid of points shown here. Supposethat, starting at th...
 1.22: In 21, how many different paths are therefrom A to B that go throug...
 1.23: A psychology laboratory conducting dreamresearch contains 3 rooms, ...
 1.24: Expand (3x2 + y)5.
 1.25: The game of bridge is played by 4 players, each ofwhom is dealt 13 ...
 1.26: Expand (x1 + 2x2 + 3x3)4.
 1.27: If 12 people are to be divided into 3 committees ofrespective sizes...
 1.28: If 8 new teachers are to be divided among 4schools, how many divisi...
 1.29: Ten weight lifters are competing in a team weightliftingcontest. Of...
 1.30: Delegates from 10 countries, including Russia,France, England, and ...
 1.31: If 8 identical blackboards are to be divided among4 schools, how ma...
 1.32: An elevator starts at the basement with 8 people(not including the ...
 1.33: We have 20 thousand dollars that must be investedamong 4 possible o...
Solutions for Chapter 1: First Course in Probability 8th Edition
Full solutions for First Course in Probability  8th Edition
ISBN: 9780136033134
Solutions for Chapter 1
Get Full SolutionsThis textbook survival guide was created for the textbook: First Course in Probability, edition: 8. Since 33 problems in chapter 1 have been answered, more than 6838 students have viewed full stepbystep solutions from this chapter. First Course in Probability was written by and is associated to the ISBN: 9780136033134. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1 includes 33 full stepbystep solutions.

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 chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

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

Analytic study
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

Assignable cause
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.

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).

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

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.

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Contingency table.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

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.

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).

Distribution function
Another name for a cumulative distribution function.

Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Momentgenerating function