 14.1: Sample spaces. For each of the following, list the sample space an...
 14.2: Sample spaces. For each of the following, list the sample space an...
 14.3: Roulette. A casino claims that its roulette wheel is trulyrandom. W...
 14.4: Rain. The weather reporter on TV makes predictionssuch as a 25% cha...
 14.5: Winter. Comment on the following quotation:What I think is our best...
 14.6: Snow. After an unusually dry autumn, a radio announcer is heard to...
 14.7: Cold streak. A batter who had failed to get a hit inseven consecuti...
 14.8: Crash. Commercial airplanes have an excellent safetyrecord. Neverth...
 14.9: Fire insurance. Insurance companies collect annualpayments from hom...
 14.10: Jackpot. On January 20, 2000, the International GamingTechnology co...
 14.11: Spinner. The plastic arrow on a spinner for a childsgame stops rota...
 14.12: Scratch off. Many stores run secret sales: Shoppersreceive cards th...
 14.13: Vehicles. Suppose that 46% of families living in acertain county ow...
 14.14: Homes. Funding for many schools comes from taxesbased on assessed v...
 14.15: Speeders. Traffic checks on a certain section of highway suggest t...
 14.16: Lefties. Although its hard to be definitive in classifying people ...
 14.17: College admissions. For high school students graduating in 2007, c...
 14.18: College admissions II. In Exercise 17, we saw thatin 2007 Harvard a...
 14.19: Car repairs. A consumer organization estimates thatover a 1year pe...
 14.20: Stats projects. In a large Introductory Statistics lecturehall, the...
 14.21: More repairs. Consider again the auto repair rates described in Ex...
 14.22: Another project. You are assigned to be part of a groupof three stu...
 14.23: Repairs, again. You used the Multiplication Ruleto calculate repair...
 14.24: Final project. You used the Multiplication Rule tocalculate probabi...
 14.25: Energy 2007. A Gallup poll in March 2007 asked 1005U.S. adults whet...
 14.26: Failing fathers? A Pew Research poll in 2007 asked2020 U.S. adults ...
 14.27: More energy. Exercise 25 shows the results of a GallupPoll about en...
 14.28: Fathers revisited. Consider again the results of thepoll about fath...
 14.29: Polling. As mentioned in the chapter, opinionpollingorganizations ...
 14.30: Polling, part II. According to Pew Research, the contact rate (pro...
 14.31: M&Ms. The Masterfoods company says that before theintroduction of p...
 14.32: Blood. The American Red Cross says that about 45% ofthe U.S. popula...
 14.33: Disjoint or independent? In Exercise 31 you calculated probabiliti...
 14.34: Disjoint or independent? In Exercise 32 you calculated probabiliti...
 14.35: Dice. You roll a fair die three times. What is the probability tha...
 14.36: Slot machine. A slot machine has three wheels thatspin independentl...
 14.37: Champion bowler. A certain bowler can bowl a strike70% of the time....
 14.38: The train. To get to work, a commuter must cross traintracks. The t...
 14.39: Voters. Suppose that in your city 37% of the voters areregistered a...
 14.40: Religion. Census reports for a city indicate that 62%of residents c...
 14.41: Tires. You bought a new set of four tires from a manufacturer who ...
 14.42: Pepsi. For a sales promotion, the manufacturer placeswinning symbol...
 14.43: 9/11? On September 11, 2002, the first anniversary ofthe terrorist ...
 14.44: Red cards. You shuffle a deck of cards and then startturning them o...
Solutions for Chapter 14: From Randomness to Probability
Full solutions for Stats: Modeling The World  3rd Edition
ISBN: 9780131359581
Solutions for Chapter 14: From Randomness to Probability
Get Full SolutionsThis textbook survival guide was created for the textbook: Stats: Modeling The World , edition: 3. Since 44 problems in chapter 14: From Randomness to Probability have been answered, more than 38839 students have viewed full stepbystep solutions from this chapter. Chapter 14: From Randomness to Probability includes 44 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Stats: Modeling The World was written by and is associated to the ISBN: 9780131359581.

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.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

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

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.

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

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol 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 incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

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 matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Crossed factors
Another name for factors that are arranged in a factorial experiment.

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Dependent variable
The response variable in regression or a designed experiment.

Dispersion
The amount of variability exhibited by data

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).

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

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

Generator
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.