 3.3.1: When the health department tested private wells in a county for two...
 3.3.2: You and a friend play a game where you each toss a balanced coin. I...
 3.3.3: A group of four components is known to contain two defectives. An i...
 3.3.4: Consider a system of water flowing through valves from A to B. (See...
 3.3.5: A problem in a test given to small children asks them to match each...
 3.3.6: Five balls, numbered 1, 2, 3, 4, and 5, are placed in an urn. Two b...
 3.3.7: Each of three balls are randomly placed into one of three bowls. Fi...
 3.3.8: A single cell can either die, with probability .1, or split into tw...
 3.3.9: In order to verify the accuracy of their financial accounts, compan...
 3.3.11: Persons entering a blood bank are such that 1 in 3 have type O+ blo...
 3.3.12: Let Y be a random variable with p(y) given in the accompanying tabl...
 3.3.13: Refer to the cointossing game in Exercise 3.2. Calculate the mean ...
 3.3.14: The maximum patent life for a new drug is 17 years. Subtracting the...
 3.3.15: An insurance company issues a oneyear $1000 policy insuring agains...
 3.3.16: The secretary in Exercise 2.121 was given n computer passwords and ...
 3.3.17: Refer to Exercise 3.7. Find the mean and standard deviation for Y =...
 3.3.18: Refer to Exercise 3.8. What is the mean number of cells in the seco...
 3.3.19: Who is the king of late night TV? An Internet survey estimates that...
 3.3.21: The number N of residential homes that a fire company can serve dep...
 3.3.22: A single fair die is tossed once. Let Y be the number facing up. Fi...
 3.3.23: In a gambling game a person draws a single card from an ordinary 52...
 3.3.24: Approximately 10% of the glass bottles coming off a production line...
 3.3.25: Two construction contracts are to be randomly assigned to one or mo...
 3.3.26: A heavyequipment salesperson can contact either one or two custome...
 3.3.27: A potential customer for an $85,000 fire insurance policy possesses...
 3.3.28: Refer to Exercise 3.3. If the cost of testing a component is $2 and...
 3.3.29: If Y is a discrete random variable that assigns positive probabilit...
 3.3.31: Suppose that Y is a discrete random variable with mean and variance...
 3.3.32: Suppose that Y is a discrete random variable with mean and variance...
 3.3.33: Let Y be a discrete random variable with mean and variance 2. If a ...
 3.3.34: The manager of a stockroom in a factory has constructed the followi...
 3.3.35: Consider the population of voters described in Example 3.6. Suppose...
 3.3.36: The manufacturer of a lowcalorie dairy drink wishes to compare the...
 3.3.37: In 2003, the average combined SAT score (math and verbal) for colle...
 3.3.38: a A meteorologist in Denver recorded Y = the number of days of rain...
 3.3.39: A complex electronic system is built with a certain number of backu...
 3.3.41: A multiplechoice examination has 15 questions, each with five poss...
 3.3.42: Refer to Exercise 3.41. What is the probability that a student answ...
 3.3.43: Many utility companies promote energy conservation by offering disc...
 3.3.44: A new surgical procedure is successful with a probability of p. Ass...
 3.3.45: A firedetection device utilizes three temperaturesensitive cells ...
 3.3.46: Construct probability histograms for the binomial probability distr...
 3.3.47: Use Table 1, Appendix 3, to construct a probability histogram for t...
 3.3.48: In Exercise 2.151, you considered a model for the World Series. Two...
 3.3.49: TaySachs disease is a genetic disorder that is usually fatal in yo...
 3.3.51: In the 18th century, the Chevalier de Mere asked Blaise Pascal to c...
 3.3.52: The taste test for PTC (phenylthiocarbamide) is a favorite exercise...
 3.3.53: A manufacturer of floor wax has developed two new brands, A and B, ...
 3.3.54: Suppose that Y is a binomial random variable based on n trials with...
 3.3.55: Suppose that Y is a binomial random variable with n > 2 trials and ...
 3.3.56: An oil exploration firm is formed with enough capital to finance te...
 3.3.57: Refer to Exercise 3.56. Suppose the firm has a fixed cost of $20,00...
 3.3.58: A particular concentration of a chemical found in polluted water ha...
 3.3.59: Ten motors are packaged for sale in a certain warehouse. The motors...
 3.3.61: A particular sale involves four items randomly selected from a larg...
 3.3.62: Goranson and Hall (1980) explain that the probability of detecting ...
 3.3.63: Consider the binomial distribution with n trials and P(S) = p. a Sh...
 3.3.64: Consider an extension of the situation discussed in Example 3.10. I...
 3.3.65: Refer to Exercise 3.64. The maximum likelihood estimator for p is Y...
 3.3.66: Suppose that Y is a random variable with a geometric distribution. ...
 3.3.67: Suppose that 30% of the applicants for a certain industrial job pos...
 3.3.68: Refer to Exercise 3.67. What is the expected number of applicants w...
 3.3.69: About six months into George W. Bushs second term as president, a G...
 3.3.71: Let Y denote a geometric random variable with probability of succes...
 3.3.72: Given that we have already tossed a balanced coin ten times and obt...
 3.3.73: A certified public accountant (CPA) has found that nine of ten comp...
 3.3.74: Refer to Exercise 3.73. What are the mean and standard deviation of...
 3.3.75: The probability of a customer arrival at a grocery service counter ...
 3.3.76: Of a population of consumers, 60% are reputed to prefer a particula...
 3.3.77: If Y has a geometric distribution with success probability p, show ...
 3.3.78: If Y has a geometric distribution with success probability .3, what...
 3.3.79: How many times would you expect to toss a balanced coin in order to...
 3.3.81: In responding to a survey question on a sensitive topic (such as Ha...
 3.3.82: Refer to Exercise 3.70. The prospector drills holes until he finds ...
 3.3.83: The secretary in Exercises 2.121 and 3.16 was given n computer pass...
 3.3.84: Refer to Exercise 3.83. Find the mean and the variance of Y , the n...
 3.3.85: Find E[Y (Y 1)] for a geometric random variable Y by finding d2/dq2...
 3.3.86: Consider an extension of the situation discussed in Example 3.13. I...
 3.3.87: Refer to Exercise 3.86. The maximum likelihood estimator for p is 1...
 3.3.88: If Y is a geometric random variable, define Y = Y 1. If Y is interp...
 3.3.89: Refer to Exercise 3.88. Derive the mean and variance of the random ...
 3.3.91: Refer to Exercise 3.90. If each test costs $20, find the expected v...
 3.3.92: Ten percent of the engines manufactured on an assembly line are def...
 3.3.93: Refer to Exercise 3.92. What is the probability that the third nond...
 3.3.94: Refer to Exercise 3.92. Find the mean and variance of the number of...
 3.3.95: Refer to Exercise 3.92. Given that the first two engines tested wer...
 3.3.96: The telephone lines serving an airline reservation office are all b...
 3.3.97: A geological study indicates that an exploratory oil well should st...
 3.3.98: Consider the negative binomial distribution given in Definition 3.9...
 3.3.99: In a sequence of independent identical trials with two possible out...
 3.3.101: a We observe a sequence of independent identical trials with two po...
 3.3.102: An urn contains ten marbles, of which five are green, two are blue,...
 3.3.103: An urn contains ten marbles, of which five are green, two are blue,...
 3.3.104: Twenty identical looking packets of white power are such that 15 co...
 3.3.105: In southern California, a growing number of individuals pursuing te...
 3.3.106: Refer to Exercise 3.103. The company repairs the defective ones at ...
 3.3.107: Seed are often treated with fungicides to protect them in poor drai...
 3.3.108: A shipment of 20 cameras includes 3 that are defective. What is the...
 3.3.109: A group of six software packages available to solve a linear progra...
 3.3.111: Specifications call for a thermistor to test out at between 9000 an...
 3.3.112: Used photocopy machines are returned to the supplier, cleaned, and ...
 3.3.113: A jury of 6 persons was selected from a group of 20 potential juror...
 3.3.114: Refer to Exercise 3.113. If the selection process were really rando...
 3.3.115: Suppose that a radio contains six transistors, two of which are def...
 3.3.116: Simulate the experiment described in Exercise 3.115 by marking six ...
 3.3.117: In an assemblyline production of industrial robots, gearbox assemb...
 3.3.118: Five cards are dealt at random and without replacement from a stand...
 3.3.119: Cards are dealt at random and without replacement from a standard 5...
 3.3.121: Let Y denote a random variable that has a Poisson distribution with...
 3.3.122: Customers arrive at a checkout counter in a department store accord...
 3.3.123: The random variable Y has a Poisson distribution and is such that p...
 3.3.124: Approximately 4% of silicon wafers produced by a manufacturer have ...
 3.3.125: Refer to Exercise 3.122. If it takes approximately ten minutes to s...
 3.3.126: Refer to Exercise 3.122. Assume that arrivals occur according to a ...
 3.3.127: The number of typing errors made by a typist has a Poisson distribu...
 3.3.128: Cars arrive at a toll both according to a Poisson process with mean...
 3.3.129: Refer to Exercise 3.128. How long can the attendants phone call las...
 3.3.131: The number of knots in a particular type of wood has a Poisson dist...
 3.3.132: The mean number of automobiles entering a mountain tunnel per twom...
 3.3.133: Assume that the tunnel in Exercise 3.132 is observed during ten two...
 3.3.134: Consider a binomial experiment for n = 20, p = .05. Use Table 1, Ap...
 3.3.135: A salesperson has found that the probability of a sale on a single ...
 3.3.136: Increased research and discussion have focused on the number of ill...
 3.3.137: The probability that a mouse inoculated with a serum will contract ...
 3.3.138: Let Y have a Poisson distribution with mean . Find E[Y (Y 1)] and t...
 3.3.139: In the daily production of a certain kind of rope, the number of de...
 3.3.141: A food manufacturer uses an extruder (a machine that produces bite...
 3.3.142: Let p(y) denote the probability function associated with a Poisson ...
 3.3.143: Refer to Exercise 3.142 (c). If the number of phone calls to the fi...
 3.3.144: Refer to Exercises 3.142 and 3.143. If the number of phone calls to...
 3.3.145: If Y has a binomial distribution with n trials and probability of s...
 3.3.146: Differentiate the momentgenerating function in Exercise 3.145 to f...
 3.3.147: If Y has a geometric distribution with probability of success p, sh...
 3.3.148: Differentiate the momentgenerating function in Exercise 3.147 to f...
 3.3.149: Refer to Exercise 3.145. Use the uniqueness of momentgenerating fu...
 3.3.151: Refer to Exercise 3.145. If Y has momentgenerating function m(t) =...
 3.3.152: Refer to Example 3.23. If Y has momentgenerating function m(t) = e...
 3.3.153: Find the distributions of the random variables that have each of th...
 3.3.154: Refer to Exercise 3.153. By inspection, give the mean and variance ...
 3.3.155: Let m(t) = (1/6)et + (2/6)e2t + (3/6)e3t . Find the following: a E(...
 3.3.156: Suppose that Y is a random variable with momentgenerating function...
 3.3.157: Refer to Exercise 3.156. a If W = 3Y , use the momentgenerating fu...
 3.3.158: If Y is a random variable with momentgenerating function m(t) and ...
 3.3.159: Use the result in Exercise 3.158 to prove that, if W = aY + b, then...
 3.3.161: Refer to Exercises 3.147 and 3.158. If Y has a geometric distributi...
 3.3.162: Let r(t) = ln[m(t)] and r(k) (0) denote the kth derivative of r(t) ...
 3.3.163: Use the results of Exercise 3.162 to find the mean and variance of ...
 3.3.164: Let Y denote a binomial random variable with n trials and probabili...
 3.3.165: Let Y denote a Poisson random variable with mean . Find the probabi...
 3.3.166: Refer to Exercise 3.165. Use the probabilitygenerating function fo...
 3.3.167: Let Y be a random variable with mean 11 and variance 9. Using Tcheb...
 3.3.168: Would you rather take a multiplechoice test or a fullrecall test?...
 3.3.169: This exercise demonstrates that, in general, the results provided b...
 3.3.171: For a certain type of soil the number of wireworms per cubic foot h...
 3.3.172: Refer to Exercise 3.115. Using the probability histogram, find the ...
 3.3.173: A balanced coin is tossed three times. Let Y equal the number of he...
 3.3.174: Suppose that a coin was definitely unbalanced and that the probabil...
 3.3.175: In May 2005, Tony Blair was elected to an historic third term as th...
 3.3.176: A national poll of 549 teenagers (aged 13 to 17) by the Gallop poll...
 3.3.177: For a certain section of a pine forest, the number of diseased tree...
 3.3.178: It is known that 10% of a brand of television tubes will burn out b...
 3.3.179: Refer to Exercise 3.91. In this exercise, we determined that the me...
 3.3.181: Sampling for defectives from large lots of manufactured product yie...
 3.3.182: Refer to Exercise 3.181. Use Table 1, Appendix 3, to construct the ...
 3.3.183: A quality control engineer wishes to study alternative sampling pla...
 3.3.184: A city commissioner claims that 80% of the people living in the cit...
 3.3.185: Twenty students are asked to select an integer between 1 and 10. Ei...
 3.3.186: Refer to Exercises 3.67 and 3.68. Let Y denote the number of the tr...
 3.3.187: Consider the following game: A player throws a fair die repeatedly ...
 3.3.188: If Y is a binomial random variable based on n trials and success pr...
 3.3.189: A starter motor used in a space vehicle has a high rate of reliabil...
 3.3.191: oss a balanced die and let Y be the number of dots observed on the ...
 3.3.192: oss a balanced die and let Y be the number of dots observed on the ...
 3.3.193: Two assembly lines I and II have the same rate of defectives in the...
 3.3.194: One concern of a gambler is that she will go broke before achieving...
 3.3.195: The number of imperfections in the weave of a certain textile has a...
 3.3.196: Refer to Exercise 3.195. The cost of repairing the imperfections in...
 3.3.197: The number of bacteria colonies of a certain type in samples of pol...
 3.3.198: One model for plant competition assumes that there is a zone of res...
 3.3.199: Insulindependent diabetes (IDD) is a common chronic disorder in ch...
 3.3.201: Refer to Exercises 3.103 and 3.106. In what interval would you expe...
 3.3.202: The number of cars driving past a parking area in a oneminute time...
 3.3.203: A type of bacteria cell divides at a constant rate over time. (That...
 3.3.204: The probability that any single driver will turn left at an interse...
 3.3.205: An experiment consists of tossing a fair die until a 6 occurs four ...
 3.3.206: Accident records collected by an automobile insurance company give ...
 3.3.207: The number of people entering the intensive care unit at a hospital...
 3.3.208: A recent survey suggests that Americans anticipate a reduction in l...
 3.3.209: A supplier of heavy construction equipment has found that new custo...
 3.3.211: A merchant stocks a certain perishable item. She knows that on any ...
 3.3.212: Show that the hypergeometric probability function approaches the bi...
 3.3.213: A lot of N = 100 industrial products contains 40 defectives. Let Y ...
 3.3.214: A lot of N = 100 industrial products contains 40 defectives. Let Y ...
 3.3.215: It is known that 5% of the members of a population have disease A, ...
 3.3.216: Let Y have a hypergeometric distribution p(y) = r y Nr ny N n , y =...
 3.3.217: Use the result derived in Exercise 3.216(c) and Definition 3.4 to d...
 3.3.218: Use the result derived in Exercise 3.216(c) and Definition 3.4 to d...
Solutions for Chapter 3: Discrete Random Variables and Their Probability Distributions
Full solutions for Mathematical Statistics with Applications  7th Edition
ISBN: 9780495110811
Solutions for Chapter 3: Discrete Random Variables and Their Probability Distributions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. Chapter 3: Discrete Random Variables and Their Probability Distributions includes 197 full stepbystep solutions. Since 197 problems in chapter 3: Discrete Random Variables and Their Probability Distributions have been answered, more than 204431 students have viewed full stepbystep solutions from this chapter.

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.

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.

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.

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.

Bayes’ 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.

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

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

Combination.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

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

Continuity correction.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

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.

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

Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Fraction defective control chart
See P chart

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 .