Probability And Statistics For Engineering And The Sciences 7th Edition Dave Ellis, Jay L Devore - Solutions

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=+this with the corresponding maximum transferable load (kN) as measured in the laboratory.The data is given here:Calc: Meas: Calc: Meas:14.2 13.7 14.3 13.4 16.0 13.7 21.4 21.4 16.5 15.4 17.6 14.8 15.9 15.4 8.6 7.4 18.8 16.2 10.3 7.4 17.9 16.3 11.9 14.7 13.1 13.7 18.7 18.2 15.4 16.2
=+the article “Interfacial Bond Strength Characteristics of FRP and RC Substrate” (J. of Compos.Constr., 2012: 35–43), investigators developed a method to mathematically model bond strength between a carbon FRP and a concrete substrate.For each of 15 carbon FRP–concrete samples, the
=+12. Historically, reinforced concrete structures used externally bonded steel plates to add strength and support. Recently, fiber reinforced polymer(FRP) plates have been used instead of steel plates because of their superior properties. In
=+ Based on this, compute the sample correlation coefficient and interpret its value. How would you characterize this correlation—as strong, moderate, or weak?
=+296–299) reported on an investigation in which lead hip internal peak rotational velocity (x) and trailing hip peak external rotational velocity (y)were determined for a sample of 15 golfers. Data provided by the article’s authors was used to calculate the following summary quantities:^(xi 2
=+11. Torsion during external rotation and extension of the hip may explain why acetabular labral tears occur in professional athletes. The article“Hip Rotational Velocities During the Full Golf Swing” (J. of Sports Sci. and Med., 2009:
=+c. Calculate the value of the sample correlation coefficient. Does it confirm your impression from the scatterplot?
=+b. Construct a scatterplot of the data. What does it suggest about the general nature of the relationship between Cl and Co?
=+a. Construct boxplots of both the clockwise and counterclockwise direction observations, and comment on any interesting features.
=+Subj: 1 2 3 4 5 6 7 Cl: 57.9 35.7 54.5 56.8 51.1 70.8 77.3 Co: 44.2 52.1 60.2 52.7 47.2 65.6 71.4 Subj: 8 9 10 11 12 13 14 Cl: 51.6 54.7 63.6 59.2 59.2 55.8 38.5 Co: 48.8 53.1 66.3 59.8 47.5 64.5 34.5
=+angles of the head in the clockwise anterior, posterior, right, and left directions for 14 randomly selected subjects. Consider the accompanying data on average anterior maximum inclination angle (AMIA) in both the clockwise (Cl) and counterclockwise (Co) directions.
=+10. Head movement evaluations are important because individuals, especially those who are disabled, may be able to operate communications aids in this manner. The article “Constancy of Head Turning Recorded in Healthy Young Humans” (J. of Biomed. Engr., 2008: 428–436)reported data on
=+f. Distance from a Stanford University student’s home town to campus and grade point average
=+e. Fuel efficiency and 3-year operating cost
=+d. Vehicle speed (mph, from 20 to 100) and fuel efficiency (mpg)
=+c. Incomes of husbands and wives when both have full-time jobs
=+a. Maximum daily temperature and cooling cost
=+9. For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or little or no correlation.Explain your choice.
=+ Construct a scatterplot of the data. How would you describe the nature of the relationship between the two variables? Does it seem to be the case that COI and API are closely related?
=+ Consider the following monthly API and statewide crude oil index (COI) values for California during 2010−11, obtained from the California Department of Transportation.COI API COI API 385.1 415.1 474.3 477.1 408.0 377.0 483.4 488.9 400.8 402.8 504.9 586.3 426.0 427.3 616.1 634.7 437.0 436.9
=+factors. From about the mid-1990s to 2010, Kentucky’s annual average API and DPI were found to be closely related to the annual average crude oil price. Based on this, the authors suggested that crude oil price could be used to predict API and DPI (“Prices of Highway Resurfacing Projects in
=+8. Researchers considered how the construction cost of highway resurfacing projects in Kentucky were affected by that state’s asphalt price index(API) and diesel price index (DPI) among other
=+ Construct a scatterplot of the data. How would you describe the nature of the relationship between the two variables?
=+researchers propose a generalized water yield model for watersheds. One important watershedspecific component of the model is , a coefficient characterizing the watershed’s annual water yield response to annual precipitation. The article provided the following data from 16 California coastal
=+7. In surface water hydrology, a common problem is the estimation of long-term annual yield from ungauged watersheds. In the article “Generalized Mediterranean Annual Water Yield Model:Grunsky’s Equation and Long-Term Average Temperature” (J. Hydrol. Engr., 2011: 874–879),
=+ Construct a scatterplot of the data. How would you describe the nature of the relationship between the two variables?
=+6. Calcium phosphate cement is gaining increasing attention for use in bone repair applications. The article “Short-Fibre Reinforcement of Calcium Phosphate Bone Cement” (J. of Engr. in Med., 2007: 203–211) reported on a study in which polypropylene fibers were used in an attempt to improve
=+c. What do the plots of parts (a) and (b) suggest about the nature of the relationship between the two variables?
=+b. Construct a scatterplot in which the axes intersect at (55, 100), as was done in the cited article. Does this plot seem preferable to the one in part (a)? Explain your reasoning.
=+a. Construct a scatterplot in which the axes intersect at (0, 0). Mark 0, 20, 40, 60, 80, and 100 on the horizontal axis and 0, 50, 100, 150, 200, and 250 on the vertical axis.
=+cheese, not the poor cousin widely available in the United States.x: 59 63 68 72 74 78 83 y: 118 182 247 208 197 135 132
=+5. The article “Objective Measurement of the Stretch-ability of Mozzarella Cheese” (J. of Texture Studies, 1992: 185–194) reported on an experiment to investigate how the behavior of mozzarella cheese varied with temperature. Consider the accompanying data on x 5 temperature and y 5
=+c. Construct a scatterplot of the data. Does it appear that recovered oil could be accurately predicted by the value of added oil? Explain your reasoning.
=+b. Do the values of the recovered oil appear to be perfectly linearly related to the added oil values?Why or why not?
=+a. For each observation, determine the percentage of oil recovery by wheat straw. Is this percentage relatively constant across all observations? Was the percentage higher at certain added oil levels over others?
=+Its Effect on Biodegradation” (J. Hazard. Toxic Radioact. Waste, 2012: 75–78), researchers examined how wheat straw could be used to extract crude oil from a water surface. An experiment was conducted in which crude oil (0 to 16.9 g)was added to 100 mL of saltwater in separate Petri dishes.
=+4. Open water oil spills, such as the Deepwater Horizon spill of 2010, can wreak terrible consequences on the environment and be expensive to clean up. Many physical and biological methods have been developed to recover oil from water surfaces. In the article “Capacity of Straw for Repeated
=+3. In the article referenced in Exercise 2, the relationship between the number of beds in a barrack and the cost of the building was also investigated.Number of Beds Cost 22 418,930 40 609,386 40 755,489 38 660,527 24 864,438 54 1,003,495 59 895,947 98 1,461,549 106 1,899,494 142 2,331,632 190
=+c. Construct a scatterplot of the data. Does it appear that cost could be accurately predicted by the value of floor area? Explain your reasoning.
=+b. Do the values of cost appear to be perfectly linearly related to the floor area values?
=+a. Construct stem-and-leaf displays of both floor area and cost. Comment on any interesting features.
=+2. The article “Case Adaptation Method of Case-Based Reasoning for Construction Cost Estimation in Korea” (J. Constr. Engr. Mgmt., 2012: 43–52) provided data on military barrack projects undertaken by the Korean Ministry of National Defense from 2004 to 2008. Two variables of interest were
=+Solar Absorptance: .81 .78 .69 .65 .48 Create a scatterplot for this data. How would you characterize the relationship between these two variables? Is the desired inverse relationship between temUnless otherwise noted, all content on this page is © Cengage Learning.perature and absorptance
=+1. In the article “Analysis of the Thermal Properties of Air-Conditioning-Type Building Materials” (Solar Energy, 2012: 2967–2974), researchers investigated thermal properties of building materials that are used across a variety of climate regions. One property of interest was solar
Consider the non-component-wise transformation\[y_{i} \mapsto \frac{y_{i}^{\lambda}}{\lambda \dot{y}^{\lambda-1}}\]where \(\dot{y}\) is the geometric mean of the components of \(y \in \mathbb{R}_{+}^{n}\). Using the result of the previous exercise, show that the modified transformation is
For the setting of the previous exercise, show that \(Y\) is distributed according to the mixture with density\[m(y)=(1-ho) \phi(y)+ho \psi(y)+o(ho)=\phi(y)(1-ho+ho \zeta(y))+o(ho)\]where \(\psi(\cdot)\) is a probability density, \(\zeta(y)=\psi(y) / \phi(y)\) is the density ratio, and
In the setting of the previous exercise, let \(W=L \varepsilon\), where \(L\) is a Boolean matrix. Show that \(W\) is a process defined on general planar regions and that it coincides with the process described at the end of Sect. 16.9.1.
Use the Gaussian model with second moments given in the previous exercise to compute a pseudo-log likelihood l0(β,σ)l0(β,σ) for the parameter (β,σ)(β,σ). Show that the pseudo log-likelihood differs from the correct log
McCullagh and Nelder (1989, Sect. 14.5) describe an experiment by S. Arnold and P. Verrell on the interbreeding of southern Appalachian mountain dusky salamanders. Each male has six breeding opportunities and each female also has six opportunities. The incomplete crossed design is shown in Table
Use the table () function to extract the distinct values for vowel diversity, consonant diversity, tone diversity and total phoneme diversity. What does this tell you?
Consider the following statement taken from Sect. 5.5. Any credible analysis that accommodates the virtual randomization must be invariant with respect to the same group, and similar remarks apply to numerical conclusions regarding temporal trends, variance components or other effects. Invariance
Procedural invariance. Consider a sample of 512 observations generated according to the model in the previous exercise. The estimation procedure is invariant if \(\hat{\beta}(Y)=\hat{\beta}\left(Y^{\tau}\right)\) and \(\hat{\sigma}(Y)=\hat{\sigma}\left(Y^{\tau}\right)\) for every baseline
For the model with persistent aviary patterns described at the end of Sect. 5.4.2, compute and plot the REML profile \(\log\) likelihood for \(\tau\) in the range \(0.5 \leq \tau \leq 24\). Use PC1 as the response, and (5.2) for the mean-value subspace. The covariance should be a linear combination
114. Show that if A1, A2, and A3 are independent events, then P(A1⏐ A2 A3) P(A1)
113. A box contains the following four slips of paper, each having exactly the same dimensions: (1) win prize 1; (2) win prize 2; (3) win prize 3; (4) win prizes 1, 2, and 3. One slip will be randomly selected. Let A1 {win prize 1}, A2 {win prize 2}, and A3 {win prize 3}. Show that A1 and A2
112. Consider four independent events A1, A2, A3, and A4 and let pi P(Ai) for i 1, 2, 3, 4. Express the probability that at least one of these four events occurs in terms of the pis, and do the same for the probability that at least two of the events occur.
111. A personnel manager is to interview four candidates for a job. These are ranked 1, 2, 3, and 4 in order of preference and will be interviewed in random order. However, at the conclusion of each interview, the manager will know only how the current candidate compares to those previously
110. A particular airline has 10 A.M. flights from Chicago to New York, Atlanta, and Los Angeles. Let A denote the event that the New York flight is full and define events B and C analogously for the other two flights. Suppose P(A) .6, P(B) .5, P(C) .4 and the three events are independent.
109. Four engineers, A, B, C, and D, have been scheduled for job interviews at 10 A.M. on Friday, January 13, at Random Sampling, Inc. The personnel manager has scheduled the four for interview rooms 1, 2, 3, and 4, respectively.However, the manager’s secretary does not know this, so assigns them
108. In a Little League baseball game, team A’s pitcher throws a strike 50% of the time and a ball 50% of the time, successive pitches are independent of one another, and the pitcher never hits a batter. Knowing this, team B’s manager has instructed the first batter not to swing at
107. A subject is allowed a sequence of glimpses to detect a target. Let Gi {the target is detected on the ith glimpse}, with pi P(Gi). Suppose the Gis are independent events and write an expression for the probability that the target has been detected by the end of the nth glimpse. [Note:This
106. One method used to distinguish between granitic (G) and basaltic (B) rocks is to examine a portion of the infrared spectrum of the sun’s energy reflected from the rock surface.Let R1, R2, and R3 denote measured spectrum intensities at
105. Disregarding the possibility of a February 29 birthday, suppose a randomly selected individual is equally likely to have been born on any one of the other 365 days.a. If ten people are randomly selected, what is the probability that all have different birthdays? That at least two have the same
104. A company uses three different assembly lines—A1, A2, and A3—to manufacture a particular component. Of those manufactured by line A1, 5% need rework to remedy a defect, whereas 8% of A2’s components need rework and 10% of A3’s need rework. Suppose that 50% of all components are
103. Refer to Exercise 102. Suppose that 50% of the overnight parcels are sent via express mail service E2 and the remaining 10% are sent via E3. Of those sent via E2, only 1% arrive late, whereas 5% of the parcels handled by E3 arrive late.a. What is the probability that a randomly selected parcel
102. A certain company sends 40% of its overnight mail parcels via express mail service E1. Of these parcels, 2% arrive after the guaranteed delivery time (denote the event “late delivery” by L). If a record of an overnight mailing is randomly selected from the company’s file, what is the
101. A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is .9, the probability that at least one of the two components does so is .96, and the probability that both components do so is .75. Given that the first
100. One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5%detection rate for noncarriers. Suppose the test is applied independently to two different blood samples from the same
b. Given that a fastener passed inspection, what is the probability that it passed the initial inspection and did not need recrimping?
a. What is the probability that a randomly selected incoming fastener will pass inspection either initially or after recrimping?
99. Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 95% of all fasteners pass an initial inspection. Of the 5% that fail, 20% are so seriously defective that they must be scrapped. The remaining fasteners are
98. Each contestant on a quiz show is asked to specify one of six possible categories from which questions will be asked.Suppose P(contestant requests category i) 1 6 and successive contestants choose their categories independently of one another. If there are three contestants on each show and
97. A chemical engineer is interested in determining whether a certain trace impurity is present in a product. An experiment has a probability of .80 of detecting the impurity if it is present. The probability of not detecting the impurity if it is absent is .90. The prior probabilities of the
95. Individual A has a circle of five close friends (B, C, D, E, and F). A has heard a certain rumor from outside the circle and has invited the five friends to a party to circulate the rumor. To begin, A selects one of the five at random and tells 96. Refer to Exercise 95. If at each stage the
94. A transmitter is sending a message by using a binary code, namely, a sequence of 0’s and 1’s. Each transmitted bit (0 or 1) must pass through three relays to reach the receiver. At each relay, the probability is .20 that the bit sent will be different from the bit received (a reversal).
93. One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air Force Base in California. Let A denote the event that the Vandenberg launch goes off on schedule, and let B represent the event that the Cape Canaveral launch goes off
92. An employee of the records office at a certain university currently has ten forms on his desk awaiting processing. Six of these are withdrawal petitions and the other four are course substitution requests.a. If he randomly selects six of these forms to give to a subordinate, what is the
c. Given that the selected can had a surface defect, what is the probability that it came from line 1?
b. If the selected can came from line 1, what is the probability that it had a blemish?
a. What is the probability that the can was produced by line 1? That the reason for nonconformance is a crack?
91. A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three lines during a particular time period.Line 1 Line 2 Line 3 Blemish 15 12 20 Crack 50 44 40
90. A small manufacturing company will start operating a night shift. There are 20 machinists employed by the company.a. If a night crew consists of 3 machinists, how many different crews are possible?b. If the machinists are ranked 1, 2, . . . , 20 in order of competence, how many of these crews
89. Suppose identical tags are placed on both the left ear and the right ear of a fox. The fox is then let loose for a period of time. Consider the two events C1 {left ear tag is lost} and C2 {right ear tag is lost}. Let P(C1) P(C2), and assume C1 and C2 are independent events. Derive an
88. Professor Stan der Deviation can take one of two routes on his way home from work. On the first route, there are four railroad crossings. The probability that he will be stopped by
87. Refer to the assumptions stated in Exercise 80 and answer the question posed there for the system in the accompanying picture. How would the probability change if this were a subsystem connected in parallel to the subsystem pictured in Figure 2.14(a)?
86.a. A lumber company has just taken delivery on a lot of 10,000 2 4 boards. Suppose that 20% of these boards(2,000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other. Let A {the first board is green} and B {the second
85. A quality control inspector is inspecting newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration.Given that a flaw is actually present, let p denote the probability that the flaw is detected during any one
84. Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive vehicles pass or fail independently of one another, calculate the following probabilities:a. P(all of the next three vehicles inspected pass)b. P(at least one of the
83. Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 90% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on
82. Consider independently rolling two fair dice, one red and the other green. Let A be the event that the red die shows 3 dots, B be the event that the green die shows 4 dots, and C be the event that the total number of dots showing on the two dice is 7. Are these events pairwise independent
81. Refer back to the series-parallel system configuration introduced in Example 2.35, and suppose that there are only two cells rather than three in each parallel subsystem [in Figure 2.14(a), eliminate cells 3 and 6, and renumber cells 4 and 5 as 3 and 4]. Using P(Ai) .9, the probability that
80. Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works;
79. Two pumps connected in parallel fail independently of one another on any given day. The probability that only the older pump will fail is .10, and the probability that only the newer pump will fail is .05. What is the probability that the pumping system will fail on any given day (which happens
78. A boiler has five identical relief valves. The probability that any particular valve will open on demand is .95. Assuming independent operation of the valves, calculate P(at least one valve opens) and P(at least one valve fails to open).
77. An aircraft seam requires 25 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability.a. If 20% of all seams need reworking, what is the probability that a rivet is defective?b. How
76. The probability that a grader will make a marking error on any particular question of a multiple-choice exam is .1. If there are ten questions and questions are marked independently, what is the probability that no errors are made? That at least one error is made? If there are n questions and
75. One of the assumptions underlying the theory of control charting (see Chapter 16) is that successive plotted points are independent of one another. Each plotted point can signal either that a manufacturing process is operating correctly or that there is some sort of malfunction. Even when a
74. Suppose that the proportions of blood phenotypes in a particular population are as follows:A B AB O.42 .10 .04 .44 Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? What is the probability that
73. If A and B are independent events, show that A and B are also independent. [Hint: First establish a relationship between P(A B), P(B), and P(A B).]
72. In Exercise 13, is any Ai independent of any other Aj?Answer using the multiplication property for independent events.

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Probability And Statistics For Engineering And The Sciences 7th Edition Dave Ellis, Jay L Devore - Solutions

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