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

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 possible approximation to the probability that X is between 15 and 20, inclusive.
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 certain type. The stated contents was 135 oz.a. What is the probability that a single jar contains
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 condition of any particular board is independent of that of any other board.a. What is the approximate
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 diameter distribution with mean value 3.04 cm and standard deviation .02 cm. Acceptable corks have
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 sec?c. Compute the expected reaction time.d. Compute the standard deviation of reaction time.e. If an
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 which the reaction takes place? If not, is the median temperature smaller or larger than 0?d. Suppose
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 After an Eruption" (Marine Biology, 2011: 181-192) proposed the following mixture of normal
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 experiment involving the exposure of carbon manganese steel to acidified seawater.F (x; α, β) = e -e -(x-
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 â‰¤ 1).b. Calculate P(.5 â‰¤ X â‰¤ 1).c. Calculate P(X > 1.5).e. Obtain the density function f (x).f. Calculate E(X).g. Calculate V(X) and ÏƒX.h. If the borrower
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 uncertainty in t by regarding it as a normally distributed random variable with mean value μ and
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 θ have a single mode? Why or why not?c. What is the mode of an exponential distribution with
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 approximated by an exponential distribution. Let X 5 the lateral position error (nautical miles), which can be
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 for modeling the behavior of what the authors called "the criticality level of a situation" X.This
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 itemized deductions on a randomly chosen form. Assume that X has the pdfa. Find the value of k. What
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 particular unit of measurement), so that current gain = X = ln(I0/Ii). Assume X is normally
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 strength (MPa) of composites under specified conditions can be mo deled by a Weibull distribution with
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 then differentiate it with respect to y.
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 / 60. Use this to obtain the cdf of Y and then differentiate to obtain the pdf.b. If X has a gamma
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 solved for x to yield x = k(y). Then it can be shown that the pdf of Y isg(y) = f [k(y)] ∙
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 µ̃ = 0.
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 independent of one another, each with a normal distribution having mean 0 and variance Ïƒ2. It can then
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 questions regarding birth coincidences.a. Disregarding leap year and assuming that the other 365
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 + âˆ†x) is approximately f (x) âˆ™ âˆ†x. The conditional probability that it fails in (x, x + âˆ†x) given that it has lasted at least 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 that X has an exponential distribution with parameter λ. [The cdf of X is F(x) = P(X ≤ x); X ≤
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) + gꞌ(m) ∙ (X - m)The right-hand side of this equation is a linear function of X. If the distribution of
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 line at x lies entirely on or below the graph. (See the figure below.) How does g(Î¼) = g(E(X))
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 P(X ≤ g(y)), use the fact that X has a cdf of the form in Expression (4.12), and differentiate
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 a credit card. An article in the Los Angeles Times gave data which suggested that a beta
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 Planning and Management, 2006: 4-14), the runoff volume willbe 0 if V ≤ νd and will be k(V - νd)
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 different traffic environment, the distribution of time headway has the forma. Determine the value of
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 depth (cm) of the bioturbation layer in sediment in a certain region.a. What are the mean and variance
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 â‰¤ .5) [i.e., F(.5)]?c. Using the cdf from (a), what is P(.25d. What is the 75th percentile of the distribution?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 waiting time X could be modeled with the following pdf:a. Graph f (x; Î¸, 80) for the three cases
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 and .5, so the limiter output is a random variable Y related to X by Y = X if |X| ≤ .5, Y = .5 if
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 hydrologic variable. What is a. P(X ‰¤ 1)? b. P(1 ‰¤ X ‰¤ 3)? c. The pdf
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 ≤ X ≤ 3).d. For k satisfying -5 < k < k + 4 < 5, compute P (k < X < k + 4).
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 â‰¤ y b. Obtain an expression for the (100p)th percentile. [Consider separately 0 c. Compute E(Y) and V(Y). How do these compare with the expected
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 µ̃?c. Compute E(X) and V(X).d. If 1.5 thousand gallons are in stock at the beginning of the week
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 = 1.8ºC + 32.]
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) = kÎ¸2 (k - 1)-2 (k - 2)-1.d. If k = 2, what can you say about V(X)?e. What conditions on k are necessary to ensure that E(Xn) is finite?
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 µ̃ + 32 is the median of the Y distribution.b. How is the 90th percentile of the Y distribution
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 approximated by a continuous distribution with pdf f(x) = k(1 + x / 2.5) 27 for x ≤ 0.a. What is the
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 uniformly distributed on [0, 360]. Define Y to be the transformed variable Y = h(X) = (2π / 360) X-
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 ≤ Z ≤ 2.50)e. P(Z ≤ 1.37)f. P(-1.75 ≤ Z)g. P(-1.50 ≤ Z ≤ 2.00)h. P(1.37 ≤ Z ≤
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 ≤ |Z|) = .016
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 probabilities by standardizing and then using Table A.3.a. P(X ≤ 15)b. P(X ≤ 17.5)c. P(X ≥ 10)d.
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 Speed of Automatic Transmission Mopeds in Periodic Motor Vehicle Inspections" (J. of Automobile Engr.,
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 = .30 and σ = .06. a. What is the probability that the concentration exceeds .50? b. What is the
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 Stochastic Construction Activities for Simulation" (J. of Construction Engr. and Mgmnt.,2013: 1037-1045)
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 2,4DFormulation and Quinclorac on Spray Droplet Size and Deposition" (Weed Technology, 2005: 1030-1036)
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 Blood," J. of Med. Engr. and Tech., 2006: 25-30, including a normal probability plot as described in
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 second machine produces corks with diameters that have a normal distribution with mean 3.04 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 Corroding Pipelines Considering Multiple Failure Modes and Time Dependent Internal Pressure" (J. 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 Engr., 1982: 107-111) proposes the Rayleigh distribution, with pdfas a model for the X
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 with μ = 43 and σ = 4.5. a. What is the probability that yield strength is at most 40? Greater than
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 mean value 200 m and standard deviation 30 m. Equipment damage will occur if the parachute opens at an
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 the value of θ have to be to ensure that 95% of all readings are within .1° of μ?
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 Bridge Engr., 2013: 735-747). a. If 5% of all vehicles travel less than 39.12 m/h and 10% travel
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 value? c. Between 1 and 2 SDs from its mean value?
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 a particular alloy is normally distributed with mean 70 and standard deviation 3. a. If a specimen
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 will be a surcharge. What value of c is such that 99% of all parcels are at least 1 lb under the
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 negative? What property of the standard normal curve justifies your answer?
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 with mean 3432 g and standard deviation 482 g. [The article "Are Babies Normal?" (The American
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 the end of the lecture and suppose the pdf of X isa. Find the value of k and draw the corresponding
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 levels and increase the amount of more beneficial polyunsaturated fat. The company claims that 97 out
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 Exercise 44 in Chapter 3 for an interpretation). Obtain this probability in the case of a normal
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 correction to calculate the probability that the number of flaws is a. Between 20 and 30, inclusive. b. At
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, .6, and .8 and compare to the exact probabilities calculated from Appendix Table A.1. a. P(15 ≤ X
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 the number among these that are nonconforming and can be reworked. What is the (approximate)
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 drivers in the sample regularly wear a seat belt? b. Fewer than 400 of those in the sample regularly wear
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., E(Y) and V(Y)]? [Write the cdf of Y, P(Y ≤ y), as an integral involving the pdf of X, and then
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 Integer Coefficients" (Mathematics of Computation, 1977: 214-222). For 0The relative error of this
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 = 1), compute the following: a. The expected time between two successive arrivals b. The standard
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 k. c. What is the probability that the actual tracking weight is greater than the prescribed
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 with parameter λ = .01386 (as suggested in the article "Competition and Dispersal from Multiple
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 Planning with Analytical Probabilistic Models, 2000, p. 69). a. What is the probability that the duration
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 daily sea-ice advance/retreat from each sensor is similar and is approximately double exponential." 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 in duration and then 10¢ for each additional minute exceeding 20 (assume that calls lasting a non
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 distribution specified in (d).
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 with mean value 37.5 ms and standard deviation 21.6 (suggested by the article "Computation Time of
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 amounts to shifting the density curves in Figure 4.27 so that they begin their ascent or descent at γ
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. What is the probability that a transistor will last between 12 and 24 weeks? b. What is the
The special case of the gamma distribution in which Î± is a positive integer n is called an Erlang distribution. If we replace Î² by 1/ Î» in Expression (4.8), the Erlang pdf is
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 distributed with Î» = .01 and that components fail independently of one another. Define
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 distribution with A = .20 and B = 4.25 for the diameter X of a certain type of weld (mm). a. Determine the
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). Then differentiate this with respect to y to obtain the pdf of X2 [the square of a N (0, 1) variable].
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 ≤ X ≤ 6) (This Weibull distribution is suggested as a model for time in service in "On the
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 widely used in statistical problems relating to aging of solid insulating materials subjected to
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 Multitype Branching Process Models for Emerging Epidemics" (J. of Applied Probability, 2011: 173-188)
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 parameter values are μ = 1.9 and σ =.9. a. What are the mean value and standard deviation of
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 = .8. a. What are the mean value and standard deviation of lifetime? b. What is the probability that
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 the Weibull distribution with α = 1.817 and β = .863 as a model for 1-hour significant wave height
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 enter at well-defined and regulated points. The article "Assessing Uncertainty in Mass Balance

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