All Matches
Solution Library
Expert Answer
Textbooks
Search Textbook questions, tutors and Books
Oops, something went wrong!
Change your search query and then try again
Toggle navigation
FREE Trial
S
Books
FREE
Tutors
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Ask a Question
AI Study Help
New
Search
Search
Sign In
Register
study help
mathematics
statistics
Questions and Answers of
Statistics
The negative binomial rv X was defined as the number of F's preceding the rth S. Let Y = the number of trials necessary to obtain the rth S. In the same manner in which the pmf of X was derived,
Of all customers purchasing automatic garage-door openers, 75% purchase a chain-driven model. Let X = the number among the next 15 purchasers who select the chain-driven model. a. What is the pmf of
In some applications the distribution of a discrete rv Xresembles the Poisson distribution except that zero is not a possible value of X. For example, let X = the number of tattoos t hat an
A k-out-of-n system is one that will function if and only if at least k of the n individual components in the system function. If individual components function independently of one another, each
The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables: a. T = the total number of pumps
A manufacturer of integrated circuit chips wishes to control the quality of its product by rejecting any batch in which the proportion of defective chips is too high. To this end, out of each batch
Of the people passing through an airport metal detector, .5% activate it; let X = the number among a randomly selected group of 500 who activate the detector. a. What is the (approximate) pmf of
An educational consulting firm is trying to decide whether high school students who have never before used a hand-held calculator can solve a certain type of problem more easily with a calculator
Consider a disease whose presence can be identified by carrying out a blood test. Let p denote the probability that a randomly selected individual has the disease. Suppose n individuals are
Let p1 denote the probability that any particular code symbol is erroneously transmitted through a communication system. Assume that on different symbols, errors occur independently of one another.
The purchaser of a power-generating unit requires c consecutive successful start-ups before the unit will be accepted. Assume that the outcomes of individual startups are independent of one another.
A plan for an executive travelers' club has been developed by an airline on the premise that 10% of its current customers would qualify for membership. a. Assuming the validity of this premise, among
Forty percent of seeds from maize (modern-day corn) ears carry single spikelets, and the other 60% carry paired spikelets. A seed with single spikelets will produce an ear with single spikelets 29%
A trial has just resulted in a hung jury because eight members of the jury were in favor of a guilty verdict and the other four were for acquittal. If the jurors leave the jury room in random order
A reservation service employs five information operators who receive requests for information independently of one another, each according to a Poisson process with rate a = 2 per minute. a. What is
Let X be the number of students who show up for a professor's office hour on a particular day. Suppose that the pmf of X is p(0) = .20, p(1) = .25, p(2) = .30, p(3) = .15, and p(4) = .10. a. Draw the
Grasshoppers are distributed at random in a large field according to a Poisson process with parameter a = 2 per square yard. How large should the radius R of a circular sampling region be taken so
A newsstand has ordered five copies of a certain issue of a photography magazine. Let X = the number of individuals who come in to purchase this magazine. If X has a Poisson distribution with
Individuals A and B begin to play a sequence of chess games. Let S = {A wins a game}, and suppose that outcomes of successive games are independent with P(S) = p and P(F) = 1 - p (they never draw).
A test for the presence of a certain disease has probability .20 of giving a false-positive reading (indicating that an individual has the disease when this is not the case) and probability .10 of
The generalized negative binomial pmf is given by nb(x; r, p) 5 k(r, x) ? pr(1 - p)x x = 0, 1, 2,... Let X, the number of plants of a certain species found in a particular region, have this
There are two Certified Public Accountants in a particular office who prepare tax returns for clients. Suppose that for a particular type of complex form, the number of errors made by the first
The mode of a discrete random variable X with pmf p(x) is that value x* for which p(x) is largest (the most probablex value). a. Let X~Bin(n, p). By considering the ratio b(x + 1; n,p)/b(x; n, p),
A computer disk storage device has ten concentric tracks, numbered 1, 2,..., 10 from outermost to innermost, and a single access arm. Let pi = the probability that any particular request for data
If X is a hypergeometric rv, show directly from the definition that E(X) = nM/N (consider only the case n < M). [Hint: Factor nM/N out of the sum for E(X), and show that the terms inside the sum are
Use the fact thatto prove Chebyshev's inequality given in Exercise 44.
Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the
The simple Poisson process of Section 3.6 is characterized by a constant rate α at which events occur per unit time. A generalization of this is to suppose that the probability of
Consider a collection A1, ... , Ak of mutually exclusive and exhaustive events, and a random variable X whose distribution depends on which of the Ai's occurs (e.g., a commuter might select one of
Consider a communication source that transmits packets containing digitized speech. After each transmission, the receiver sends a message indicating whether the transmission was successful or
A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature of the project) in applying for a building permit. Let Y 5 the number
Many manufacturers have quality control programs that include inspection of incoming materials for defects. Suppose a computer manufacturer receives circuit boards in batches of five. Two boards are
Some parts of California are particularly earth quake prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at
A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have
Two fair six-sided dice are tossed independently. Let M = the maximum of the two tosses (so M(1,5) = 5, M(3,3) = 3, etc.). a. What is the pmf of M? [Hint: First determine p(1), then p(2), and so
A library subscribes to two different weekly news magazines, each of which is supposed to arrive in Wednesday's mail. In actuality, each one may arrive on Wednesday, Thursday, Friday, or Saturday.
Give three examples of Bernoulli rv's (other than those in the text).
Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is .4 (a
Suppose that you read through this year's issues of the New York Times and record each number that appears in a news article-the income of a CEO, the number of cases of wine produced by a winery, the
Refer to Exercise 13, and calculate and graph the cdf F(x). Then use it to calculate the probabilities of the events given in parts (a)-(d) of that problem.
A branch of a certain bank in New York City has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows:Calculate the following probabilities
An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X 5 the number of months between successive payments. The cdf of
In Example 3.12, let Y = the number of girls born before the experiment terminates. With p = P (B) and 1 - p = P (G), what is the pmf of Y? [Hint: First list the possible values of Y, starting with
Alvie Singer lives at 0 in the accompanying diagram and has four friends who live at A, B, C, and D. One day Alvie decides to go visiting, so he tosses a fair coin twice to decide which of the four
After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. At the beginning of the next lecture, the professor distributes the four
Show that the cdf F(x) is a non-decreasing function; that is, x1, x2 implies that F(x1) # F(x2). Under what condition will F(x1) 5 F(x2)?
The pmf of the amount of memory X (GB) in a purchased flash drive was given in Example 3.13 asCompute the following: a. E(X) b. V(X) directly from the definition c. The standard deviation of X d.
Using the experiment in Example 3.3, define two more random variables and list the possible values of each.
An individual who has automobile insurance from acertain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of
Refer to Exercise 12 and calculate V(Y) and σY. Then determine the probability that Y is within 1 standard deviation of its mean value.
A certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X 5 the rated capacity of a freezer of this brand sold at a certain store. Suppose
Let X be a Bernoulli rv with pmf as in Example 3.18. a. Compute E(X2). b. Show that V(X) = p(1 - p). c. Compute E(X79).
Suppose that the number of plants of a particular type found in a rectangular sampling region (called a quadrat by ecologists) in a certain geographic area is an rv X with pmfIs E(X) finite? Justify
A small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with pmfSuppose the store owner actually pays $2.00 for each copy of the magazine
Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities .8, .1, .08, and .02, respectively. A
The n candidates for a job have been ranked 1, 2, 3,..., n. Let X = the rank of a randomly selected candidate, so that X has pmf(this is called the discrete uniform distribution). Compute E(X) and
Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities .15, .35, .35, and .15, respectively. a.
A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 5-lb batches. Let X = the number of batches ordered by a randomly chosen customer, and
Let X 5 the number of nonzero digits in a randomly selected 4-digit PIN that has no restriction on the digits. What are the possible values of X? Give three possible outcomes and their associated X
a. Draw a line graph of the pmf of X in Exercise 35. Then determine the pmf of - X and draw its line graph. From these two pictures, what can you say about V(X) and V (- X)?b. Use the proposition
Use the definition in Expression (3.13) to prove that V (aX + b) = σ2 - σX2
Suppose E(X) = 5 and E[X(X - 1)] = 27.5. What isa. E(X2)? [Hint: First verify that E[X(X - 1)] = E(X2) - E(X)]?b. V(X)?c. The general relationship among the quantities E(X), E[X(X - 1)], and V(X)?
Write a general rule for E(X - c) where c is a constant. What happens when c = µ, the expected value of X?
A result called Chebyshev's inequality states that for any probability distribution of an rv X and any number k that is at least 1, P(|X - µ| > kσ) < 1/k2. In words, the probability that the value
If a < X < b, show that a < E(X) < b.
Compute the following binomial probabilities directly from the formula for b(x; n, p): a. b (3; 8, .35) b. b (5; 8, .6) c. P (3 < X < 5) when n = 7 and p = .6 d. P (1 < X) when n = 9 and p = .1
The article "Should You Report That Fender- Bender?" (Consumer Reports, Sept. 2013: 15) reported that 7 in 10 auto accidents involve a single vehicle (the article recommended always reporting to the
NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 25 children and let X be the number in the sample
A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as "seconds." a. Among six randomly selected goblets, how likely is it
If the sample space S is an infinite set, does this necessarily imply that any rv X defined from S will have an infinite set of possible values? If yes, say why. If no, give an example.
A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. What is
Refer to the previous exercise. a. What is the expected number of calls among the 25 that involve a fax message? b. What is the standard deviation of the number among the 25 calls that involve a fax
Suppose that 30% of all students who have to buy a text for a particular course want a new copy (the successes!), whereas the other 70% want a used copy. Consider randomly selecting 25 purchasers. a.
Exercise 30 (Section 3.3) gave the pmf of Y, the number of traffic citations for a randomly selected individual insured by a particular company. What is the probability that among 15 randomly chosen
A particular type of tennis racket comes in a midsize version and an oversize version. Sixty percent of all customers at a certain store want the oversize version. a. Among ten randomly selected
Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 60% can be repaired, whereas the other 40% must be replaced with new units. If a company
The College Board reports that 2% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities (Los Angeles Times, July 16,
A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have acceptable voltages. Suppose that 90% of all batteries from a certain supplier
A very large batch of components has arrived at a distributor. The batch can be characterized as acceptable only if the proportion of defective components is at most .10. The distributor decides to
An ordinance requiring that a smoke detector be installed in all previously constructed houses has been in effect in a particular city for 1 year. The fire department is concerned that many houses
A toll bridge charges $1.00 for passenger cars and $2.50 for other vehicles. Suppose that during daytime hours, 60% of all vehicles are passenger cars. If 25 vehicles cross the bridge during a
A student who is trying to write a paper for a course has a choice of two topics, A and B. If topic A is chosen, the student will order two books through interlibrary loan, whereas if topic B is
a. For fixed n, are there values of p (0 < p < 1) for which V(X) = 0? Explain why this is so. b. For what value of p is V(X) maximized?
a. Show that b(x; n, 1 - p) = b(n - x; n, p). b. Show that B(x; n, 1 - p) = 1 - B(n - x - 1; n, p). c. What do parts (a) and (b) imply about the necessity of including values of p greater than .5 in
Show that E(X) = np when X is a binomial random variable. [First express E(X) as a sum with lower limit x = 1. Then factor out np, let y = x - 1 so that the sum is from y = 0 to y = n - 1, and show
Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices, with P(A) = .5, P(B) = .2, and P(C) = .3. a. Among the
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous
Refer to Chebyshev's inequality given in Exercise 44. Calculate P( |X - µ| > kσ) for k = 2 and k = 3 when X~ Bin (20, .5), and compare to the corresponding upper bound. Repeat for X~Bin (20,
Eighteen individuals are scheduled to take a driving test at a particular DMV office on a certain day, eight of whom will be taking the test for the first time. Suppose that six of these individuals
Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 7 of these
For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete.a. X = the number of unbroken eggs in a randomly chosen
An instructor who taught two sections of engineering statistics last term, the first with 20 students and the second with 30, decided to assign a term project. After all project shad been turned in,
A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the specimens for analysis.a. What is the
A personnel director interviewing 11 senior engineers for four job openings has scheduled six interviews for the first day and five for the second day of interviewing. Assume that the candidates are
Twenty pairs of individuals playing in a bridge tournament have been seeded 1, ... , 20. In the first part of the tournament, the 20 are randomly divided into 10 east- west pairs and 10 north-south
A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 50 industrial firms. An inspector will visit 10 randomly selected firms to check for violations of
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function:a. Graph the pdf and verify that the total area under the density
A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and θ, both > 0, and
Let X denote the time to failure (in years) of a certain hydraulic component. Suppose the pdf of X is f(x) = 32 / (x + 4)3 for x < 0.a. Verify that f (x) is a legitimate pdf.b. Determine the
The completion time X for a certain task has cdf F(x) given bya. Obtain the pdf f(x) and sketch its graph.b. Compute P(.5 ≤ X ≤ 2).c. Compute E(X).
Showing 73900 - 74000
of 82267
First
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
Last