 2.2.1: Suppose a family contains two children of different ages, and we ar...
 2.2.2: Suppose that A and B are two events. Write expressions involving un...
 2.2.3: Draw Venn diagrams to verify DeMorgans laws. That is, for any two s...
 2.2.4: If A and B are two sets, draw Venn diagrams to verify the following...
 2.2.5: Refer to Exercise 2.4. Use the identities A = A S and S = B B and a...
 2.2.6: From a survey of 60 students attending a university, it was found t...
 2.2.7: A group of five applicants for a pair of identical jobs consists of...
 2.2.8: Suppose two dice are tossed and the numbers on the upper faces are ...
 2.2.9: Every persons blood type is A, B, AB, or O. In addition, each indiv...
 2.2.11: A sample space consists of five simple events, E1, E2, E3, E4, and ...
 2.2.12: A vehicle arriving at an intersection can turn right, turn left, or...
 2.2.13: Americans can be quite suspicious, especially when it comes to gove...
 2.2.14: A survey classified a large number of adults according to whether t...
 2.2.15: An oil prospecting firm hits oil or gas on 10% of its drillings. If...
 2.2.16: Of the volunteers coming into a blood center, 1 in 3 have O+ blood,...
 2.2.17: Hydraulic landing assemblies coming from an aircraft rework facilit...
 2.2.18: Suppose two balanced coins are tossed and the upper faces are obser...
 2.2.19: A business office orders paper supplies from one of three vendors, ...
 2.2.21: If A and B are events, use the result derived in Exercise 2.5(a) an...
 2.2.22: If A and B are events and B A, use the result derived in Exercise 2...
 2.2.23: If A and B are events and B A, why is it obvious that P(B) P(A)?
 2.2.24: Use the result in Exercise 2.22 and the Axioms in Definition 2.6 to...
 2.2.25: A single car is randomly selected from among all of those registere...
 2.2.26: Three imported wines are to be ranked from lowest to highest by a p...
 2.2.27: In Exercise 2.12 we considered a situation where cars entering an i...
 2.2.28: Four equally qualified people apply for two identical positions in ...
 2.2.29: Two additional jurors are needed to complete a jury for a criminal ...
 2.2.31: The Bureau of the Census reports that the median family income for ...
 2.2.32: Patients arriving at a hospital outpatient clinic can select one of...
 2.2.33: A boxcar contains six complex electronic systems. Two of the six ar...
 2.2.34: A retailer sells only two styles of stereo consoles, and experience...
 2.2.35: An airline has six flights from New York to California and seven fl...
 2.2.36: An assembly operation in a manufacturing plant requires three steps...
 2.2.37: A businesswoman in Philadelphia is preparing an itinerary for a vis...
 2.2.38: An upscale restaurant offers a special fixe prix menu in which, for...
 2.2.39: An experiment consists of tossing a pair of dice. a Use the combina...
 2.2.41: How many different sevendigit telephone numbers can be formed if t...
 2.2.42: A personnel director for a corporation has hired ten new engineers....
 2.2.43: A fleet of nine taxis is to be dispatched to three airports in such...
 2.2.44: Refer to Exercise 2.43. Assume that taxis are allocated to airports...
 2.2.45: Suppose that we wish to expand (x + y + z)17. What is the coefficie...
 2.2.46: Ten teams are playing in a basketball tournament. In the first roun...
 2.2.47: Refer to Exercise 2.46. If 2n teams are to be assigned to games 1, ...
 2.2.48: If we wish to expand (x + y)8, what is the coefficient of x 5 y3? W...
 2.2.49: Students attending the University of Florida can select from 130 ma...
 2.2.51: A local fraternity is conducting a raffle where 50 tickets are to b...
 2.2.52: An experimenter wishes to investigate the effect of three variables...
 2.2.53: Five firms, F1, F2,..., F5, each offer bids on three separate contr...
 2.2.54: A group of three undergraduate and five graduate students are avail...
 2.2.55: A study is to be conducted in a hospital to determine the attitudes...
 2.2.56: A student prepares for an exam by studying a list of ten problems. ...
 2.2.57: Two cards are drawn from a standard 52card playing deck. What is t...
 2.2.58: Five cards are dealt from a standard 52card deck. What is the prob...
 2.2.59: Five cards are dealt from a standard 52card deck. What is the prob...
 2.2.61: Suppose that we ask n randomly selected people whether they share y...
 2.2.62: A manufacturer has nine distinct motors in stock, two of which came...
 2.2.63: The eightmember Human Relations Advisory Board of Gainesville, Flo...
 2.2.64: A balanced die is tossed six times, and the number on the uppermost...
 2.2.65: Refer to Exercise 2.64. Suppose that the die has been altered so th...
 2.2.66: Refer to Example 2.10. What is the probability that a an ethnic gro...
 2.2.67: Refer to Example 2.13. Suppose that the number of distributors is M...
 2.2.68: Show that, for any integer n 1, a n n = 1. Interpret this result. b...
 2.2.69: Prove that n+1 k = n k + n k1 .
 2.2.71: If two events, A and B, are such that P(A) = .5, P(B) = .3, and P(A...
 2.2.72: For a certain population of employees, the percentage passing or fa...
 2.2.73: Gregor Mendel was a monk who, in 1865, suggested a theory of inheri...
 2.2.74: One hundred adults were interviewed in a telephone survey. Of inter...
 2.2.75: Cards are dealt, one at a time, from a standard 52card deck. a If ...
 2.2.76: A survey of consumers in a particular community showed that 10% wer...
 2.2.77: A study of the posttreatment behavior of a large number of drug abu...
 2.2.78: In the definition of the independence of two events, you were given...
 2.2.79: If P(A) > 0, P(B) > 0, and P(A) < P(AB), show that P(B) < P(BA).
 2.2.81: Suppose that A and B are mutually exclusive events, with P(A) > 0 a...
 2.2.82: Suppose that A B and that P(A) > 0 and P(B) > 0. Show that P(BA) =...
 2.2.83: If A and B are mutually exclusive events and P(B) > 0, show that P(...
 2.2.84: If A1, A2, and A3 are three events and P(A1 A2) = P(A1 A3) = 0 but ...
 2.2.85: If A and B are independent events, show that A and B are also indep...
 2.2.86: Suppose that A and B are two events such that P(A) = .8 and P(B) = ...
 2.2.87: Suppose that A and B are two events such that P(A) + P(B) > 1. a Wh...
 2.2.88: Suppose that A and B are two events such that P(A) = .6 and P(B) = ...
 2.2.89: Suppose that A and B are two events such that P(A) + P(B) < 1. a Wh...
 2.2.91: Can A an B be mutually exclusive if P(A) = .4 and P(B) = .7? If P(A...
 2.2.92: A policy requiring all hospital employees to take lie detector test...
 2.2.93: Two events A and B are such that P(A) = .2, P(B) = .3, and P(A B) =...
 2.2.94: A smoke detector system uses two devices, A and B. If smoke is pres...
 2.2.95: In a game, a participant is given three attempts to hit a ball. On ...
 2.2.96: If A and B are independent events with P(A) = .5 and P(B) = .2, fin...
 2.2.97: Consider the following portion of an electric circuit with three re...
 2.2.98: With relays operating as in Exercise 2.97, compare the probability ...
 2.2.99: Suppose that A and B are independent events such that the probabili...
 2.2.101: Articles coming through an inspection line are visually inspected b...
 2.2.102: Diseases I and II are prevalent among people in a certain populatio...
 2.2.103: Refer to Exercise 2.50. Hours after the rigging of the Pennsylvania...
 2.2.104: If A and B are two events, prove that P(A B) 1 P(A) P(B). [Note: Th...
 2.2.105: If the probability of injury on each individual parachute jump is ....
 2.2.106: If A and B are equally likely events and we require that the probab...
 2.2.107: Let A, B, and C be events such that P(A) > P(B) and P(C) > 0. Const...
 2.2.108: f A, B, and C are three events, use two applications of the result ...
 2.2.109: If A, B, and C are three equally likely events, what is the smalles...
 2.2.111: An advertising agency notices that approximately 1 in 50 potential ...
 2.2.112: Three radar sets, operating independently, are set to detect any ai...
 2.2.113: Consider one of the radar sets of Exercise 2.112. What is the proba...
 2.2.114: A lie detector will show a positive reading (indicate a lie) 10% of...
 2.2.115: A state autoinspection station has two inspection teams. Team 1 is...
 2.2.116: A communications network has a builtin safeguard system against fa...
 2.2.117: A football team has a probability of .75 of winning when playing an...
 2.2.118: An accident victim will die unless in the next 10 minutes he receiv...
 2.2.119: Suppose that two balanced dice are tossed repeatedly and the sum of...
 2.2.121: A new secretary has been given n computer passwords, only one of wh...
 2.2.122: Applet Exercise Use the applet Bayes Rule as a Tree to obtain the r...
 2.2.123: Applet Exercise Refer to Exercise 2.122 and Example 2.23. Suppose t...
 2.2.124: A population of voters contains 40% Republicans and 60% Democrats. ...
 2.2.125: A diagnostic test for a disease is such that it (correctly) detects...
 2.2.126: Applet Exercise Refer to Exercise 2.125. The probability that the t...
 2.2.127: Applet Exercise Refer to Exercises 2.125 and 2.126. Suppose now tha...
 2.2.128: A plane is missing and is presumed to have equal probability of goi...
 2.2.129: Males and females are observed to react differently to a given set ...
 2.2.131: The symmetric difference between two events A and B is the set of a...
 2.2.132: Use Theorem 2.8, the law of total probability, to prove the followi...
 2.2.133: A student answers a multiplechoice examination question that offer...
 2.2.134: Two methods, A and B, are available for teaching a certain industri...
 2.2.135: Of the travelers arriving at a small airport, 60% fly on major airl...
 2.2.136: A personnel director has two lists of applicants for jobs. List 1 c...
 2.2.137: Five identical bowls are labeled 1, 2, 3, 4, and 5. Bowl i contains...
 2.2.138: Following is a description of the game of craps. A player rolls two...
 2.2.139: Refer to Exercise 2.112. Let the random variable Y represent the nu...
 2.2.141: Refer again to Exercise 2.120. Let the random variable Y represent ...
 2.2.142: A spinner can land in any of four positions, A, B, C, and D, with e...
 2.2.143: Show that Theorem 2.7 holds for conditional probabilities. That is,...
 2.2.144: Let S contain four sample points, E1, E2, E3, and E4. a List all po...
 2.2.145: A patient receiving a yearly physical examination must have 18 chec...
 2.2.146: Five cards are drawn from a standard 52card playing deck. What is ...
 2.2.147: Refer to Exercise 2.146. A gambler has been dealt five cards: two a...
 2.2.148: A bin contains three components from supplier A, four from supplier...
 2.2.149: A large group of people is to be checked for two common symptoms of...
 2.2.151: A Model for the World Series Two teams A and B play a series of gam...
 2.2.152: We know the following about a colormetric method used to test lake ...
 2.2.153: Medical case histories indicate that different illnesses may produc...
 2.2.154: a A drawer contains n = 5 different and distinguishable pairs of so...
 2.2.155: A group of men possesses the three characteristics of being married...
 2.2.156: The accompanying table lists accidental deaths by age and certain s...
 2.2.157: A study of the residents of a region showed that 20% were smokers. ...
 2.2.158: A bowl contains w white balls and b black balls. One ball is select...
 2.2.159: It seems obvious that P() = 0. Show that this result follows from t...
 2.2.161: Refer to Exercise 2.160. What is the probability that the number of...
 2.2.162: Assume that there are nine parking spaces next to one another in a ...
 2.2.163: Relays used in the construction of electric circuits function prope...
 2.2.164: Refer to Exercise 2.163 and consider circuit A. If we know that cur...
 2.2.165: Refer to Exercise 2.163 and consider circuit B. If we know that cur...
 2.2.166: Eight tires of different brands are ranked from 1 to 8 (best to wor...
 2.2.167: Refer to Exercise 2.166. Let Y denote the actual quality rank of th...
 2.2.168: As in Exercises 2.166 and 2.167, eight tires of different brands ar...
 2.2.169: Three beer drinkers (say I, II, and III) are to rank four different...
 2.2.171: An AP news service story, printed in the Gainesville Sun on May 20,...
 2.2.172: Let A and B be any two events. Which of the following statements, i...
 2.2.173: As items come to the end of a production line, an inspector chooses...
 2.2.174: Many public schools are implementing a nopass, noplay rule for at...
 2.2.175: Three events, A, B, and C, are said to be mutually independent if P...
 2.2.176: Refer to Exercise 2.175 and suppose that events A, B, and C are mut...
 2.2.177: Refer to Exercise 2.90(b) where a friend claimed that if there is a...
 2.2.178: Suppose that the probability of exposure to the flu during an epide...
 2.2.179: Two gamblers bet $1 each on the successive tosses of a coin. Each h...
 2.2.181: Suppose that the streets of a city are laid out in a grid with stre...
Solutions for Chapter 2: Probability
Full solutions for Mathematical Statistics with Applications  7th Edition
ISBN: 9780495110811
Solutions for Chapter 2: Probability
Get Full SolutionsSince 163 problems in chapter 2: Probability have been answered, more than 155216 students have viewed full stepbystep solutions from this chapter. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2: Probability includes 163 full stepbystep solutions. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7.

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.

Bayesâ€™ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

Biased estimator
Unbiased estimator.

Bivariate distribution
The joint probability distribution of two random variables.

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

Comparative experiment
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

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

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.

Defectsperunit control chart
See U chart

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

Design matrix
A matrix that provides the tests that are to be conducted in an experiment.

Dispersion
The amount of variability exhibited by data

Distribution function
Another name for a cumulative distribution function.

Eficiency
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.

Error of estimation
The difference between an estimated value and the true value.

Exponential random variable
A series of tests in which changes are made to the system under study

Frequency distribution
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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

Harmonic mean
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 .