New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
mathematics
statistics

Probability And Statistics For Engineering And The Sciences 9th Edition Jay L. Devore - Solutions

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, derive the pmf of Y.
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 X? b. Compute P(X > 10). c. Compute P(6 < X < 10). d. Compute µ and σ2. e. If the store currently
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 individual wants removed when she or he arrives at a tattoo-removal facility. Suppose the pmf of X isa.
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 with probability .9, what is the probability that a 3-out-of-5 system functions?
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 in use b. X = the difference between the numbers in use at stations 1 and 2 c. U = the maximum
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 (10,000 chips), 25 will be selected and tested. If at least 5 of these 25 are defective, the entire
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 X? b. Compute P(X = 5). c. Compute P(5 < X).
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 that uses reverse Polish logic or one that does not use this logic. A sample of 25 students is selected
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 independently selected for testing. One way to proceed is to carry out a separate test on each of the n blood
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. Suppose also that with probability p2 an erroneous symbol is corrected upon receipt. Let X denote the
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. Let p denote the probability that any particular start-up is successful. The random variable of
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 25 randomly selected current customers, what is the probability that between 2 and 6 (inclusive)
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% of the time, whereas a seed with paired spikelets will produce an ear with single spikelets 26% of
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 and each of the first four leaving the room is accosted by a reporter in quest of an interview, what
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 the probability that during a given 1-min period, the first operator receives no requests? b. What
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 corresponding probability histogram. b. What is the probability that at least two students show up?
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 that the probability of finding at least one in the region equals .99?
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 parameter µ = 4, what is the expected number of copies that are sold?
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). They will play until one of them wins ten games. Let X = the number of games played (with possible
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 giving a false-negative result. Suppose that ten individuals are tested, five of whom have the disease
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 distribution with p = .3 and r = 2.5. What is P(X = 4)? What is the probability that at least one plant is
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 preparer has a Poisson distribution with mean value Âµ1, the number of errors made by the second
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), show that b(x; n, p) increases with x as long as x < np - (1 - p). Conclude that the mode x* is the
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 will take the arm to track i(i = 1,... , 10). Assume that the tracks accessed in successive seeks are
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 of the form h(y; n - 1, M - 1, N - 1), where y = x - 1.]
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 flight. The probability mass function of Y appears in the accompanying table.a. What is the
The simple Poisson process of Section 3.6 is characterized by a constant rate Î± at which events occur per unit time. A generalization of this is to suppose that the probability of exactly one event occurring in the interval [t, t + Î”t] is Î±(t) ?
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 three possible routes from home to work, with X representing the commute time). Let E(X|Ai) denote the
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 unsuccessful. If a transmission is unsuccessful, the packet is re-sent. Suppose a voice packet can be
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 of forms required of the next applicant. The probability that y forms are required is known to be
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 selected from each batch for inspection. We can represent possible outcomes of the selection process
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 random; let X denote the number among the four who have earthquake insurance. a. Find the
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 been found. Suppose that 90% of all batteries have acceptable voltages. Let Y denote the number of
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 on.] b. Determine the cdf of M and graph it.
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. Suppose the two arrive independently of one another, and for each one P (Wed.) = .3, P (Thurs.) = .4,
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 couple will travel together in the same vehicle, so either both people will be on time or else both
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 total charitable contribution of a politician during the previous tax year, the age of a celebrity,
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 directly from the cdf:a. p(2), that is, P(X = 2)b. P(X > 3)c. P(2 d. P(2 5)
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 X is as follows:a. What is the pmf of X? b. Using just the cdf, compute P(3 # X # 6) and P(4 # X).
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 the smallest, and proceed until you see a general formula.]
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 to visit. Once at a friend's house, he will either return home or else proceed to one of the two
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 books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to
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. V(X) using the shortcut formula
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 Y isa. Compute E(Y). b. Suppose an individual with Y violations incurs a surcharge of $100Y2.
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 that X has pmfa. Compute E(X), E(X2), and V(X). b. If the price of a freezer having capacity X is
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 your answer (this is another distribution that statisticians would call heavy-tailed).
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 and the price to customers is $4.00. If magazines left at the end of the week have no salvage value,
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 particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100,
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 V(X) using the shortcut formula.
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. Calculate E(X) and then E(5 - X). b. Would the repair facility be better off charging a flat fee of $75
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 suppose that X has pmfCompute E(X) and V(X). Then compute the expected number of pounds left after the
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 values.
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 involving V (aX + b) to establish a general relationship between V (X) and V (-X).
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 of X lies at least k standard deviations from its mean is at most 1/k2. a. What is the value of the
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 insurance company an accident involving multiple vehicles). Suppose 15 accidents are randomly
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 who have a food allergy. Then X ~ Bin(25, .05). a. Determine both P(X < 3) and P(X < 3). b.
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 that only one is a second? b. Among six randomly selected goblets, what is the probability that at
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 the probability that a. At most 6 of the calls involve a fax message? b. Exactly 6 of the calls
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 message? c. What is the probability that the number of calls among the 25 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. What are the mean value and standard deviation of the number who want a new copy of the book? b.
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 such individualsa. At least 10 have no citations?b. Fewer than half have at least one citation?c.
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 customers who want this type of racket, what is the probability that at least six want the oversize
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 purchases ten of these telephones, what is the probability that exactly two will end up being
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, 2002). Consider a random sample of 25 students who have recently taken the test. a. What is the
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 have acceptable voltages. Among ten randomly selected flashlights, what is the probability that at
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 randomly select 10 components and to accept the batch only if the number of defective components in
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 remain without detectors. Let p = the true proportion of such houses having detectors, and suppose
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 particular daytime period, what is the resulting expected toll revenue?
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 chosen, the student will order four books. The student believes that a good paper necessitates receiving
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 Appendix Table A.1?
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 that the sum equals 1.]
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 next 100 customers, what are the mean and variance of the number who pay with a debit card? Explain
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 records, 20% of all those making reservations do not appear for the trip. Answer the following
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, .75). In Exercise 44 A result called Chebyshev's inequality states that for any probability distribution
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 are randomly assigned to a particular examiner, and let X be the number among the six who are taking
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 refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators
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 standard egg cartonb. Y = the number of students on a class list for a particular course who are absent on
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, the instructor randomly ordered them before grading. Consider the first 15 graded projects.a. What
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 pmf of the number of granite specimens selected for analysis?b. What is the probability that all
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 interviewed in random order.a. What is the probability that x of the top four 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 pairs.a. What is the probability that x of the top 10 pairs end up playing east-west?b. What is the
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 regulations.a. If 15 of the firms are actually violating at least one regulation, what is the pmf
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 curve is indeed 1.b. Calculate P(X â‰¤ 4). How does this probability compare to P(X c. Calculate
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 Î¸, both > 0, and the pdf isa. Sketch the graph of f (x; k, Î¸).b. Verify that the total area under the graph equals
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 cdf.c. Use the result of part (b) to calculate the probability that time to failure is between 2 and 5
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 â‰¤ X â‰¤ 2).c. Compute E(X).

Showing 73900 - 74000 of 88243

First
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved