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
Let X represent the number of individuals who respond to a particular online coupon offer. Suppose that X has approximately a Wei bull distribution with α = 10 and β = 20. Calculate the best
The article "Computer Assisted Net Weight Control" (Quality Progress, 1983: 22-25) suggests a normal distribution with mean 137.2 oz and standard deviation 1.6 oz for the actual contents of jars of a
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Suppose that a batch of 250 boards has been received and that the
Exercise 38 introduced two machines that produce wine corks, the first one having a normal diameter distribution with mean value 3 cm and standard deviation .1 cm, and the second having a normal
The reaction time (in seconds) to a certain stimulus is a continuous random variable with pdfa. Obtain the cdf.b. What is the probability that reaction time is at most 2.5 sec? Between 1.5 and 2.5
Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has pdfa. Sketch the graph of f(x).b. Determine the cdf and sketch it.c. Is 0 the median temperature at
An oocyte is a female germ cell involved in reproduction. Based on analyses of a large sample, the article "Reproductive Traits of Pioneer Gastropod Species Colonizing DeepSea Hydrothermal Vents
The article "The Prediction of Corrosion by Statistical Analysis of Corrosion Profiles" (Corrosion Science, 1985: 305-315) suggests the following cdf for the depth X of the deepest pit in an
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf isa. Calculate P(X ≤ 1).b. Calculate P(.5 ≤ X ≤ 1).c. Calculate P(X > 1.5).e.
Let t = the amount of sales tax a retailer owes the government for a certain period. The article "Statistical Sampling in Tax Audits" (Statistics and the Law, 2008:320-343) proposes modeling the
The mode of a continuous distribution is the value x* that maximizes f (x).a. What is the mode of a normal distribution with parameters m and s?b. Does the uniform distribution with parameters μ and
The article "Error Distribution in Navigation" (J. of the Institute of Navigation, 1971: 429-442) suggests that the frequency distribution of positive errors (magnitudes of errors) is well
The article "Statistical Behavior Modeling for DriverAdaptive Precrash Systems" (IEEE Trans. on Intelligent Transp. Systems, 2013: 1-9) proposed the following mixture of two exponential distributions
Suppose a particular state allows individuals filing tax returns to itemize deductions only if the total of all itemized deductions is at least $5000. Let X (in 1000s of dollars) be the total of
Let Ii be the input current to a transistor and I0 be the output current. Then the current gain is proportional to ln(I0yIi). Suppose the constant of proportionality is 1 which amounts to choosing a
The article "Response of SiCf/Si3N4 Composites Under Static and Cyclic Loading-An Experimental and Statistical Analysis" (J. of Engr. Materials and Technology, 1997: 186-193) suggests that tensile
Let Z have a standard normal distribution and define a new rv Y by Y = σZ + µ. Show that Y has a normal distribution with parameters μ and σ. Y ≤ y iff Z ≤? Use this to find the cdf of Y and
a. Suppose the lifetime X of a component, when measured in hours, has a gamma distribution with parameters α and β. Let Y 5 the lifetime measured in minutes. Derive the pdf of Y. Y≤ y iff X ≤ y
In Exercises 117 and 118, as well as many other situations, one has the pdf f(x) of X and wishes to know the pdf of y = h(X). Assume that h( ∙ ) is an invertible function, so that y = h(x) can be
The cdf for X (5 measurement error) of Exercise 3 isa. Compute P (X < 0)b. Compute P (21 < X < 1)c. Compute P (.5 < X)d. Verify that f (x) is as given in Exercise 3 by obtaining F'(x).e. Verify that
Based on data from a dart-throwing experiment, the article "Shooting Darts" (Chance, Summer 1997, 16-19) proposed that the horizontal and vertical errors from aiming at a point target should be
The article "Three Sisters Give Birth on the Same Day" (Chance, Spring 2001, 23-25) used the fact that three Utah sisters had all given birth on March 11, 1998 as a basis for posing some interesting
Let X denote the lifetime of a component, with f (x) and F(x) the pdf and cdf of X. The probability that the component fails in the interval (x, x + ∆x) is approximately f (x) ∙ ∆x.
Let U have a uniform distribution on the interval [0, 1]. Then observed values having this distribution can be obtained from a computer's random number generator. Let X = - (1 / λ)ln(1 - U).a. Show
Consider an rv X with mean m and standard deviation s, and let g(X) be a specified function of X. The first-order Taylor series approximation to g(X) in the neighborhood of m isg(X) ≈ g(μ) +
A function g(x) is convex if the chord connecting any two points on the function's graph lies above the graph. When g(x) is differentiable, an equivalent condition is that for every x, the tangent
Let X have a Weibull distribution with parameters α = 2 and β. Show that Y = 2 X2 / β2 has a chi-squared distribution with ν = 2. [The cdf of Y is P(Y ≤ y); express this probability in the form
An individual's credit score is a number calculated based on that person's credit history that helps a lender determine how much he/she should be loaned or what credit limit should be established for
Let V denote rainfall volume and W denote runoff volume (both in mm). According to the article "Runoff Quality Analysis of Urban Catchments with Analytical Probability Models" (J. of Water Resource
Example 4.5 introduced the concept of time headway in traffic flow and proposed a particular distribution for X = the headway between two randomly selected consecutive cars (sec). Suppose that in a
The article "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants" (WaterResearch, 1984: 1169-1174) suggests the uniform distribution on the interval (7.5, 20) as a model for
Let X denote the amount of space occupied by an article placed in a 1-ft3 packing container. The pdf of X isa. Graph the pdf. Then obtain the cdf of X and graph it.b. What is P(X ≤ .5) [i.e.,
The article "A Model of Pedestrians' Waiting Times for Street Crossings at Signalized Intersections"(Transportation Research, 2013: 17-28) suggested that under some circumstances the distribution of
Let X have a uniform distribution on the interval [A, B].a. Obtain an expression for the (100p)th percentile.b. Compute E(X), V(X), and σX.c. For n, a positive integer, compute E(Xn).
Let X denote the voltage at the output of a microphone, and suppose that X has a uniform distribution on the interval from -1 to 1. The voltage is processed by a "hard limiter" with cutoff values -.5
Let X be a continuous rv with cdfThis type of cdf is suggested in the article "Variability in Measured Bedload Transport Rates" (Water Resources Bull., 1985: 39-48) as a model for a certain
Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = -5 and B = 5.a. Compute P(X < 0).b. Compute P (-2.5 < X < 2.5).c. Compute P (-2
Consider the pdf for total waiting time Y for two busesintroduced in Exercise 8.a. Compute and sketch the cdf of Y. [Consider separately 0 ≤ y b. Obtain an expression for the (100p)th
The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with pdfa. Compute the cdf of X.b. Obtain an expression for the (100p)th percentile. What is the value of
If the temperature at which a certain compound melts is a random variable with mean value 120ºC and standard deviation 2ºC, what are the mean temperature and standard deviation measured in ºF? ºF
Let X have the Pareto pdfintroduced in Exercise 10.a. If k > 1, compute E(X).b. What can you say about E(X) if k = 1?c. If k > 2, show that V(X) = kθ2 (k - 1)-2 (k - 2)-1.d. If k = 2, what can you
Let X be the temperature in °C at which a certain chemical reaction takes place, and let Y be the temperature in °F (so Y = 1.8 X + 32).a. If the median of the X distribution is µ̃, show that 1.8
Let X be the total medical expenses (in 1000s of dollars) incurred by a particular individual during a given year. Although X is a discrete random variable, suppose its distribution is quite well
When a dart is thrown at a circular target, consider the location of the landing point relative to the bull's eye. Let X be the angle in degrees measured from the horizontal, and assume that X is
Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate.a. P(0 ≤ Z ≤ 2.17)b. P(0 ≤ Z ≤ 1)c. P(-2.50 ≤ Z ≤ 0)d. P(-2.50
In each case, determine the value of the constant c that makes the probability statement correct.a. ϕ(c)= .9838b. P(0 ≤ Z ≤ c) = .291c. P(c ≤ Z) = .121d. P(-c ≤ Z ≤ c) = .668e. P(c ≤
The error involved in making a certain measurement is a continuous rv X with pdfa. Sketch the graph of f (x).b. Compute P(X > 0).c. Compute P (–1 < X < 1). d. Compute P(X .5).
Find the following percentiles for the standard normal distribution. Interpolate where appropriate.a. 91stb. 9thc. 75thd. 25the. 6th
Determine zα for the following values of a:a. α = .0055b. α = .09c. α = .663
Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean value 15.0 kips and standard deviation 1.25 kips. Compute the following
Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of operation, and low cost. The article "Procedure to Verify the Maximum
The article "Reliability of DomesticWaste Biofilm Reactors" (J. of Envir. Engr., 1995: 785-790) suggests that substrate concentration (mg/cm3) of influent to a reactor is normally distributed with µ
In a road-paving process, asphalt mix is delivered to the hopper of the paver by trucks that haul the material from the batching plant. The article "Modeling of Simultaneously Continuous and
Spray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of
Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 104 and standard deviation 5 (information in the article "Mathematical Modelof Chloride Concentration in Human
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation .1 cm.
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 30 mm and standard deviation 7.8 mm [suggested in the article "Reliability Evaluation of
Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. The article "Blade Fatigue Life Assessment with Application to VAWTS" (J. of Solar Energy
The article "Monte Carlo Simulation-Tool for Better Understanding of LRFD" (J. of Structural Engr., 1993: 1586-1599) suggests that yield strength (ksi) for A36 grade steel is normally distributed
The automatic opening device of a military cargo parachute has been designed to open when the parachute is 200 m above the ground. Suppose opening altitude actually has a normal distribution with
The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation θ. What would
Vehicle speed on a particular bridge in China can be modeled as normally distributed ("Fatigue Reliability Assessment for LongSpan Bridges under Combined Dynamic Loads from Winds and Vehicles," J. of
If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is a. Within 1.5 SDs of its mean value? b. Farther than 2.5 SDs from its mean
The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of
The weight distribution of parcels sent in a certain manner is normal with mean value 12 lb and standard deviation 3.5 lb. The parcel service wishes to establish a weight value c beyond which there
Suppose Appendix Table A.3 contained ϕ(z) only for z ≥ 0. Explain how you could still compute a. P(-1.72 ≤ Z ≤ - .55) b. P(-1.72 ≤ Z ≤ .55) Is it necessary to tabulate F(z) for z
Consider babies born in the "normal" range of 37-43 weeks gestational age. Extensive data supports the assumption that for such babies born in the United States, birth weight is normally distributed
A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X 5 the time that elapses between the end of the hour and
In response to concerns about nutritional contents of fast foods, McDonald's has announced that it will use a new cooking oil for its French fries that will decrease substantially trans fatty acid
Chebyshev's inequality, (Exercise 44, Chapter 3), is valid for continuous as well as discrete distributions. It states that for any number k satisfying k ≥ 1, P(|X - μ| ≥ kσ) ≤ 1/k2 (see
Let X denote the number of flaws along a 100-m reel of magnetic tape (an integer-valued variable). Suppose X has approximately a normal distribution with μ = 25 and σ = 5. Use the continuity
Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p = .5,
Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote
Suppose only 75% of all drivers in a certain state regularly wear a seat belt. A random sample of 500 drivers is selected. What is the probability that a. Between 360 and 400 (inclusive) of the
Show that the relationship between a general normal percentile and the corresponding z percentile is as stated in this section.
a. Show that if X has a normal distribution with parameters μ and θ, then Y = aX + b (a linear function of X) also has a normal distribution. What are the parameters of the distribution of Y [i.e.,
There is no nice formula for the standard normal cdf F(z), but several good approximations have been published in articles. The following is from "Approximations for Hand Calculators Using Small
Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1 (which is identical to a standard gamma distribution with α
The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with pdfa. Sketch the graph of f (x). b. Find the value of
Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution
Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2.725 hours is a good model for rainfall duration (Urban Stormwater Management
The article "Microwave Observations of Daily Antarctic Sea Ice Edge Expansion and Contribution Rates" (IEEE Geo sci. and Remote Sensing Letters, 2006: 54-58) states that "The distribution of the
A consumer is trying to decide between two long-distance calling plans. The first one charges a flat rate of 10¢ per minute, whereas the second charges a flat rate of 99¢ for calls up to 20 minutes
Evaluate the following: a. Г(6) b. Г(5/2) c. F(4; 5) (the incomplete gamma function) and F(5; 4) d. P(X ≤ 5) when X has a standard gamma distribution with α = 7. e. P(3 < X < 8) when X has the
Let X denote the data transfer time (ms) in a grid computing system (the time required for data transfer between a "worker" computer and a "master" computer. Suppose that X has a gamma distribution
The two-parameter gamma distribution can be generalized by introducing a third parameter γ, called a threshold or location parameter: replace x in (4.8) by x - γ and x ≥ 0 by x ≥ γ. This
Suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime X (in weeks) has a gamma distribution with mean 24 weeks and standard deviation 12 weeks. a.
The special case of the gamma distribution in which α is a positive integer n is called an Erlang distribution. If we replace β by 1/ λ in Expression (4.8), the
A system consists of five identical components connected in series as shown:As soon as one component fails, the entire system will fail. Suppose each component has a lifetime that is exponentially
The article "Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength" (Quality and Reliability Engr. Intl., 2012: 887-896) considered the use of a uniform
If X has an exponential distribution with parameter l, derive a general expression for the (100p)th percentile of the distribution. Then specialize to obtain the median.
a. The event {X2 ¤ y} is equivalent to what event involving X itself?b. If X has a standard normal distribution, use part (a) to write the integral that equals P(X2 ¤ y).
The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β = 3. Compute the following: a. E(X) and V(X) b. P(X ≤ 6) c. P(1.5 ≤
The authors of the article "A Probabilistic Insulation Life Model for Combined Thermal Electrical Stresses" (IEEE Trans. on Elect, Insulation, 1985: 519-522) state that "the Wei bull distribution is
Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. The article "The Probability of Containment for
Let X have a Weibull distribution with the pdf from Expression (4.11). Verify that μ = BГ(1+1/α). [In the integral for E(X), make the change of variable y = (x/β)α, so that x = By 1 / α.]
The article "The Statistics of Phytotoxic Air Pollutants" (J. of Royal Stat. Soc., 1989: 183-198) suggests the lognormal distribution as a model for SO2 concentration above a certain forest. Suppose
The authors of the article from which the data in Exercise 1.27 was extracted suggested that a reasonable probability model for drill lifetime was a lognormal distribution with μ = 4.5 and σ =
The article "On Assessing the Accuracy of Offshore Wind Turbine Reliability Based Design Loads from the Environmental Contour Method" (Intl. J. of Offshore and Polar Engr., 2005: 132-140) proposes
Nonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that
Showing 74000 - 74100
of 82267
First
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
Last