- 3.1E: When the health department tested private wells in a county for two...
- 3.2E: You and a friend play a game where you each toss a balanced coin. I...
- 3.3E: A group of four components is known to contain two defectives. An i...
- 3.4E: Consider a system of water flowing through valves from A to B. (See...
- 3.5E: A problem in a test given to small children asks them to match each...
- 3.6E: Five balls, numbered 1, 2, 3, 4, and 5, are placed in an urn. Two b...
- 3.7E: Each of three balls are randomly placed into one of three bowls. Fi...
- 3.8E: A single cell can either die, with probability .1, or split into tw...
- 3.9E: In order to verify the accuracy of their financial accounts, compan...
- 3.10E: A rental agency, which leases heavy equipment by the day, has found...
- 3.11E: Persons entering a blood bank are such that 1 in 3 have type O+ blo...
- 3.12E: Let Y be a random variable with p(y) given in the accompanying tabl...
- 3.13E: Refer to the coin-tossing game in Exercise 3.2. Calculate the mean ...
- 3.14E: The maximum patent life for a new drug is 17 years. Subtracting the...
- 3.15E: Who is the king of late night TV? An Internet survey estimates that...
- 3.16E: The secretary in Exercise 2.121 was given n computer passwords and ...
- 3.17E: Refer to Exercise 3.7. Find the mean and standard deviation for Y =...
- 3.18E: Refer to Exercise 3.8. What is the mean number of cells in the seco...
- 3.19E: An insurance company issues a one-year $1000 policy insuring agains...
- 3.20E: A manufacturing company ships its product in two different sizes of...
- 3.21E: The number N of residential homes that a fire company can serve dep...
- 3.22E: A single fair die is tossed once. Let Y be the number facing up. Fi...
- 3.23E: In a gambling game a person draws a single card from an ordinary 52...
- 3.24E: Approximately 10% of the glass bottles coming off a production line...
- 3.25E: Two construction contracts are to be randomly assigned to one or mo...
- 3.26E: A heavy-equipment salesperson can contact either one or two custome...
- 3.27E: A potential customer for an $85,000 fire insurance policy possesses...
- 3.28E: Refer to Exercise 3.3. If the cost of testing a component is $2 and...
- 3.29E: If Y is a discrete random variable that assigns positive probabilit...
- 3.30E: Suppose that Y is a discrete random variable with mean ? and varian...
- 3.31E: Suppose that Y is a discrete random variable with mean ? and varian...
- 3.32E: Suppose that Y is a discrete random variable with mean ? and varian...
- 3.33E: Let Y be a discrete random variable with mean ? and variance ? 2. I...
- 3.34E: The manager of a stockroom in a factory has constructed the followi...
- 3.35E: Consider the population of voters described in Example 3.6. Suppose...
- 3.36E: a A meteorologist in Denver recorded Y = the number of days of rain...
- 3.37E: In 2003, the average combined SAT score (math and verbal) for colle...
- 3.38E: The manufacturer of a low-calorie dairy drink wishes to compare the...
- 3.39E: A complex electronic system is built with a certain number of backu...
- 3.40E: The probability that a patient recovers from a stomach disease is ....
- 3.41E: A multiple-choice examination has 15 questions, each with five poss...
- 3.42E: Refer to Exercise 3.41. What is the probability that a student answ...
- 3.43E: Many utility companies promote energy conservation by offering disc...
- 3.44E: A new surgical procedure is successful with a probability of p. Ass...
- 3.45E: A fire-detection device utilizes three temperature-sensitive cells ...
- 3.46E: Construct probability histograms for the binomial probability distr...
- 3.47E: Use Table 1, Appendix 3, to construct a probability histogram for t...
- 3.48E: A missile protection system consists of n radar sets operating inde...
- 3.49E: A manufacturer of floor wax has developed two new brands, A and B, ...
- 3.50E: In Exercise 2.151, you considered a model for the World Series. Two...
- 3.51E: In the 18th century, the Chevalier de Mere asked Blaise Pascal to c...
- 3.52E: The taste test for PTC (phenylthiocarbamide) is a favorite exercise...
- 3.53E: Tay-Sachs disease is a genetic disorder that is usually fatal in yo...
- 3.54E: Suppose that Y is a binomial random variable based on n trials with...
- 3.55E: Suppose that Y is a binomial random variable with n > 2 trials and ...
- 3.56E: An oil exploration firm is formed with enough capital to finance te...
- 3.57E: Refer to Exercise 3.56. Suppose the firm has a fixed cost of $20,00...
- 3.58E: A particular sale involves four items randomly selected from a larg...
- 3.59E: Ten motors are packaged for sale in a certain warehouse. The motors...
- 3.60E: A particular concentration of a chemical found in polluted water ha...
- 3.61E: Of the volunteers donating blood in a clinic, 80% have the Rhesus (...
- 3.62E: Goranson and Hall (1980) explain that the probability of detecting ...
- 3.64E: Consider an extension of the situation discussed in Example 3.10. I...
- 3.65E: Refer to Exercise 3.64. The maximum likelihood estimator for p is Y...
- 3.66E: Suppose that Y is a random variable with a geometric distribution. ...
- 3.67E: Suppose that 30%of the applicants for a certain industrial job poss...
- 3.68E: Refer to Exercise 3.67. What is the expected number of applicants w...
- 3.69E: About six months into George W. Bush’s second term as president, a ...
- 3.70E: An oil prospector will drill a succession of holes in a given area ...
- 3.71E: Let Y denote a geometric random variable with probability of succes...
- 3.72E: Given that we have already tossed a balanced coin ten times and obt...
- 3.73E: A certified public accountant (CPA) has found that nine of ten comp...
- 3.74E: Refer to Exercise 3.73. What are the mean and standard deviation of...
- 3.75E: The probability of a customer arrival at a grocery service counter ...
- 3.76E: If Y has a geometric distribution with success probability .3, what...
- 3.77E: If Y has a geometric distribution with success probability p, show ...
- 3.78E: Of a population of consumers, 60% are reputed to prefer a particula...
- 3.79E: In responding to a survey question on a sensitive topic (such as “H...
- 3.80E: Two people took turns tossing a fair die until one of them tossed a...
- 3.81E: How many times would you expect to toss a balanced coin in order to...
- 3.82E: Refer to Exercise 3.70. The prospector drills holes until he finds ...
- 3.83E: The secretary in Exercises 2.121 and 3.16 was given n computer pass...
- 3.84E: Refer to Exercise 3.83. Find the mean and the variance of Y , the n...
- 3.85E: Find E[Y (Y ? 1)] for a geometric random variable Y by finding . Us...
- 3.86E: Consider an extension of the situation discussed in Example 3.13. I...
- 3.87E: Refer to Exercise 3.86. The maximum likelihood estimator for p is 1...
- 3.88E: If Y is a geometric random variable, define Y ? = Y ? 1. If Y is in...
- 3.89E: Refer to Exercise 3.88. Derive the mean and variance of the random ...
- 3.90E: The employees of a firm that manufactures insulation are being test...
- 3.91E: Refer to Exercise 3.90. If each test costs $20, find the expected v...
- 3.92E: Ten percent of the engines manufactured on an assembly line are def...
- 3.93E: Refer to Exercise 3.92. What is the probability that the third non-...
- 3.94E: Refer to Exercise 3.92. Find the mean and variance of the number of...
- 3.95E: Refer to Exercise 3.92. Given that the first two engines tested wer...
- 3.96E: The telephone lines serving an airline reservation office are all b...
- 3.97E: A geological study indicates that an exploratory oil well should st...
- 3.98E: Consider the negative binomial distribution given in Definition 3.9...
- 3.99E: In a sequence of independent identical trials with two possible out...
- 3.100E: If Y is a negative binomial random variable, define Y ? = Y ? r. If...
- 3.101E: a We observe a sequence of independent identical trials with two po...
- 3.102E: An urn contains ten marbles, of which five are green, two are blue,...
- 3.103E: A warehouse contains ten printing machines, four of which are defec...
- 3.104E: Twenty identical looking packets of white power are such that 15 co...
- 3.105E: In southern California, a growing number of individuals pursuing te...
- 3.106E: Refer to Exercise 3.103. The company repairs the defective ones at ...
- 3.107E: A group of six software packages available to solve a linear progra...
- 3.108E: A shipment of 20 cameras includes 3 that are defective. What is the...
- 3.109E: Seed are often treated with fungicides to protect them in poor drai...
- 3.110E: A corporation is sampling without replacement for n = 3 firms to de...
- 3.111E: Specifications call for a thermistor to test out at between 9000 an...
- 3.112E: Used photocopy machines are returned to the supplier, cleaned, and ...
- 3.113E: A jury of 6 persons was selected from a group of 20 potential juror...
- 3.114E: Refer to Exercise 3.113. If the selection process were really rando...
- 3.115E: Suppose that a radio contains six transistors, two of which are def...
- 3.116E: Simulate the experiment described in Exercise 3.115 by marking six ...
- 3.117E: In an assembly-line production of industrial robots, gearbox assemb...
- 3.118E: Five cards are dealt at random and without replacement from a stand...
- 3.119E: Cards are dealt at random and without replacement from a standard 5...
- 3.120E: The sizes of animal populations are often estimated by using a capt...
- 3.121E: Let Y denote a random variable that has a Poisson distribution with...
- 3.122E: Customers arrive at a checkout counter in a department store accord...
- 3.123E: The random variable Y has a Poisson distribution and is such that p...
- 3.124E: Approximately 4% of silicon wafers produced by a manufacturer have ...
- 3.125E: Refer to Exercise 3.122. If it takes approximately ten minutes to s...
- 3.126E: Refer to Exercise 3.122. Assume that arrivals occur according to a ...
- 3.127E: The number of typing errors made by a typist has a Poisson distribu...
- 3.128E: Cars arrive at a toll both according to a Poisson process with mean...
- 3.129E: Refer to Exercise 3.128. How long can the attendant’s phone call la...
- 3.130E: A parking lot has two entrances. Cars arrive at entrance I accordin...
- 3.131E: The number of knots in a particular type of wood has a Poisson dist...
- 3.132E: The mean number of automobiles entering a mountain tunnel per two-m...
- 3.133E: Assume that the tunnel in Exercise 3.132 is observed during ten two...
- 3.134E: Consider a binomial experiment for n = 20, p = .05. Use Table 1, Ap...
- 3.136E: Increased research and discussion have focused on the number of ill...
- 3.137E: The probability that a mouse inoculated with a serum will contract ...
- 3.138E: Let Y have a Poisson distribution with mean ?. Find E[Y (Y ? 1)] an...
- 3.139E: In the daily production of a certain kind of rope, the number of de...
- 3.140E: A store owner has overstocked a certain item and decides to use the...
- 3.141E: A food manufacturer uses an extruder (a machine that produces bite-...
- 3.142E: Let p(y) denote the probability function associated with a Poisson ...
- 3.143E: Refer to Exercise 3.142 (c). If the number of phone calls to the fi...
- 3.144E: Refer to Exercises 3.142 and 3.143. If the number of phone calls to...
- 3.145E: If Y has a binomial distribution with n trials and probability of s...
- 3.146E: Differentiate the moment-generating function in Exercise 3.145 to f...
- 3.147E: If Y has a geometric distribution with probability of success p, sh...
- 3.148E: Differentiate the moment-generating function in Exercise 3.147 to f...
- 3.149E: Refer to Exercise 3.145. Use the uniqueness of moment-generating fu...
- 3.150E: Refer to Exercise 3.147. Use the uniqueness of moment-generating fu...
- 3.151E: Refer to Exercise 3.145. If Y has moment-generating function m(t) =...
- 3.152E: Refer to Example 3.23. If Y has moment-generating function m(t) = e...
- 3.153E: Find the distributions of the random variables that have each of th...
- 3.154E: Refer to Exercise 3.153. By inspection, give the mean and variance ...
- 3.155E: Let m(t) = (1/6)et + (2/6)e2t + (3/6)e3t. Find the following:a E ( ...
- 3.156E: Suppose that Y is a random variable with moment-generating function...
- 3.157E: Refer to Exercise 3.156.a If W = 3Y, use the moment-generating func...
- 3.158E: If Y is a random variable with moment-generating function m(t) and ...
- 3.159E: Use the result in Exercise 3.158 to prove that, if W = aY + b, then...
- 3.160E: Suppose that Y is a binomial random variable based on n trials with...
- 3.161E: Refer to Exercises 3.147 and 3.158. If Y has a geometric distributi...
- 3.162E: Let r (t) = ln[m(t)] and r (k) (0) denote the kth derivative of r (...
- 3.163E: Use the results of Exercise 3.162 to find the mean and variance of ...
- 3.164E: Let Y denote a binomial random variable with n trials and probabili...
- 3.165E: Let Y denote a Poisson random variable with mean ?. Find the probab...
- 3.166E: Refer to Exercise 3.165. Use the probability-generating function fo...
- 3.167E: Let Y be a random variable with mean 11 and variance 9. Using Tcheb...
- 3.168E: Would you rather take a multiple-choice test or a full-recall test?...
- 3.169E: This exercise demonstrates that, in general, the results provided b...
- 3.170E: The U.S. mint produces dimes with an average diameter of .5 inch an...
- 3.171E: For a certain type of soil the number of wireworms per cubic foot h...
- 3.172E: Refer to Exercise 3.115. Using the probability histogram, find the ...
- 3.173E: A balanced coin is tossed three times. Let Y equal the number of he...
- 3.174E: Suppose that a coin was definitely unbalanced and that the probabil...
- 3.175E: In May 2005, Tony Blair was elected to an historic third term as th...
- 3.176E: A national poll of 549 teenagers (aged 13 to 17) by the Gallop poll...
- 3.177E: For a certain section of a pine forest, the number of diseased tree...
- 3.178E: It is known that 10% of a brand of television tubes will burn out b...
- 3.179E: Refer to Exercise 3.91. In this exercise, we determined that the me...
- 3.180SE: Four possibly winning numbers for a lottery—AB-4536, NH-7812, SQ-78...
- 3.181SE: Sampling for defectives from large lots of manufactured product yie...
- 3.182SE: Refer to Exercise 3.181. Use Table 1, Appendix 3, to construct the ...
- 3.183SE: A quality control engineer wishes to study alternative sampling pla...
- 3.184SE: A city commissioner claims that 80% of the people living in the cit...
- 3.185SE: Twenty students are asked to select an integer between 1 and 10. Ei...
- 3.186SE: Refer to Exercises 3.67 and 3.68. Let Y denote the number of the tr...
- 3.187SE: Consider the following game: A player throws a fair die repeatedly ...
- 3.188SE: If Y is a binomial random variable based on n trials and success pr...
- 3.189SE: A starter motor used in a space vehicle has a high rate of reliabil...
- 3.190SE: Refer to Exercise 3.115. Find ?, the expected value of Y, for the t...
- 3.191SE: Find the population variance ? 2 for Exercise 3.115 and the sample ...
- 3.192SE: Toss a balanced die and let Y be the number of dots observed on the...
- 3.193SE: Two assembly lines I and II have the same rate of defectives in the...
- 3.194SE: One concern of a gambler is that she will go broke before achieving...
- 3.195SE: The number of imperfections in the weave of a certain textile has a...
- 3.196SE: Refer to Exercise 3.195. The cost of repairing the imperfections in...
- 3.197SE: The number of bacteria colonies of a certain type in samples of pol...
- 3.198SE: One model for plant competition assumes that there is a zone of res...
- 3.199SE: Insulin-dependent diabetes (IDD) is a common chronic disorder in ch...
- 3.200SE: Using the fact that ReferenceDifferentiate the moment-generating fu...
- 3.201SE: Refer to Exercises 3.103 and 3.106. In what interval would you expe...
- 3.202SE: The number of cars driving past a parking area in a one-minute time...
- 3.203SE: A type of bacteria cell divides at a constant rate ? over time. (Th...
- 3.204SE: The probability that any single driver will turn left at an interse...
- 3.205SE: An experiment consists of tossing a fair die until a 6 occurs four ...
- 3.206SE: Accident records collected by an automobile insurance company give ...
- 3.207SE: The number of people entering the intensive care unit at a hospital...
- 3.208SE: A recent survey suggests that Americans anticipate a reduction in l...
- 3.209SE: A supplier of heavy construction equipment has found that new custo...
- 3.210SE: Calculate P(|Y ? ?| ? 2?) for the Poisson probability distribution ...
- 3.211SE: A merchant stocks a certain perishable item. She knows that on any ...
- 3.212SE: Show that the hypergeometric probability function approaches the bi...
- 3.213SE: A lot of N = 100 industrial products contains 40defectives. Let Y b...
- 3.214SE: For simplicity, let us assume that there are two kinds of drivers. ...
- 3.215SE: It is known that 5% of the members of a population have disease A, ...
- 3.216SE: Let Y have a hypergeometric distribution
- 3.217SE: Use the result derived in Exercise 3.216(c) and Definition 3.4 to d...
- 3.218SE: Use the results of Exercises 3.216(c) and 3.217 to show that, for a...
Solutions for Chapter 3: Mathematical Statistics with Applications 7th Edition
Full solutions for Mathematical Statistics with Applications | 7th Edition
ISBN: 9780495110811
Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. Chapter 3 includes 216 full step-by-step solutions. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7th. Since 216 problems in chapter 3 have been answered, more than 80376 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.
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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.
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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.
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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
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Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
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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.
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Bivariate distribution
The joint probability distribution of two random variables.
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Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
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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.
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Conidence level
Another term for the conidence coeficient.
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Continuity correction.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
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Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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Control limits
See Control chart.
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Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
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Correlation coeficient
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
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Exponential random variable
A series of tests in which changes are made to the system under study
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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
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Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
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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 .
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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.
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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 .